Inclusion Criteria:

• Pathologically confirmed recurrent (not amenable to curative treatment with local and/or systemic therapies) or metastatic (disseminated) HNSCC of the oral cavity, oropharynx, hypopharynx, and/or larynx that is considered incurable by local therapies
• Disease progression at any time during or after treatment with a platinum-containing (e.g., carboplatin or cisplatin) regimen
• Disease progression on or after treatment with an anti-PD-1/PD-L1 mAb (programmed cell death protein 1/programmed death-ligand 1 monoclonal antibody)
• Pre-study imaging that demonstrates evidence of disease progression based on investigator review of at least 2 pre-study images per RECIST 1.1, following initiation of treatment with a PD-1/PD-L1 inhibitor
• Measurable disease by CT or MRI based on Response Criteria in Solid Tumors Version 1.1 (RECIST 1.1) as verified by blinded independent central review (BICR). Tumor lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions
• ECOG performance status of 0 or 1 assessed within 7 days of the first dose of study intervention
• Male participants are eligible to participate if they agree to the following during the intervention period and for at least 1 week after the last dose of lenvatinib, 3 months after the last dose of capecitabine and paclitaxel, and and 6 months after the last dose of docetaxel:
• Refrain from donating sperm
• Be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis) and agree to remain abstinent; or must agree to use contraception unless confirmed to be azoospermic
• Contraceptive use by men should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies
• A female participant is eligible to participate if she is not pregnant or breastfeeding, and at least one of the following conditions applies:
• Is not a woman of childbearing potential (WOCBP)
• Is a WOCBP and using a contraceptive method that is highly effective (with a failure rate of <1% per year), with low user dependency or be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis), during the intervention period and for at least 120 days post pembrolizumab or 1 month post lenvatinib, whichever occurs last (Arms 1 and 3), or during the intervention period and for at least 6 months after the last dose of capecitabine, docetaxel, paclitaxel; and 2 months after the last dose of cetuximab (Arm 2)
• Female participants who randomize to Arm 2 must also agree not to donate or freeze/store eggs during the intervention period and for at least 6 months after the last dose of capecitabine, docetaxel, paclitaxel; and 2 months after the last dose of cetuximab
• Adequately controlled blood pressure (BP) with or without antihypertensive medications
• Participants who are hepatitis B surface antigen (HBsAg) positive are eligible if they have received hepatitis B virus (HBV) antiviral therapy for at least 4 weeks and have undetectable HBV viral load prior to randomization
• Participants with history of hepatitis C virus (HCV) infection are eligible if HCV viral load is undetectable at screening
• Adequate organ function

Exclusion Criteria:

• Disease that is suitable for local therapy administered with curative intent
• Life expectancy of less than 3 months and/or has rapidly progressing disease in the opinion of the treating investigator
• History of (noninfectious) pneumonitis/interstitial lung disease that required steroids, or has current pneumonitis/interstitial lung disease
• Active infection requiring systemic therapy
• Diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug
• Known active central nervous system (CNS) metastases and/or carcinomatous meningitis
• Known additional malignancy that is progressing or has required active systemic treatment within the past 3 years, except basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer, or carcinoma in situ that have undergone potentially curative therapy
• Active autoimmune disease that has required systemic treatment in the past 2 years
• Had an allogeneic tissue/solid organ transplant
• Known history of human immunodeficiency virus (HIV) infection
• History of any contraindication or has a severe hypersensitivity to any components of pembrolizumab, lenvatinib or SOC chemotherapy.
• Pre-existing ≥Grade 3 gastrointestinal or non-gastrointestinal fistula
• History of a gastrointestinal malabsorption or any other condition or procedure that may affect oral study drug absorption
• Had major surgery within 3 weeks prior to first dose of study interventions
• Clinically significant cardiovascular impairment within 12 months of the first dose of study drug
• Active tuberculosis
• Has difficulty swallowing capsules or ingesting a suspension orally, or by a feeding tube
• Prior treatment with lenvatinib
• Prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to Study Day 1 or has not recovered from adverse events (AEs) due to a previously administered agent. Participants with endocrine-related AEs Grade ≤2 requiring treatment or hormone replacement may be eligible
• Has received a live or live attenuated vaccine within 30 days prior to the first dose of study intervention. Note: Administration of killed vaccines is allowed
• Previously treated with 4 or more systemic regimens given for recurrent/metastatic disease
• Has received an investigational agent or has used an investigational device within 4 weeks prior to study intervention administration
• Known psychiatric or substance abuse disorder that would interfere with the participant's ability to cooperate with the requirements of the study

Inclusion Criteria:

• Eight years or older with HNC diagnosis confirmed histologically o Stage 1-3 HNC pathologically confirmed diagnosis of squamous cell carcinoma of the oropharynx, larynx, hypopharynx, nasopharyngeal, or oral cavity
• Plan to receive radiotherapy (>60 Gy), chemo-irradiation or bio-radiation either as primary or as a post-operative treatment to the head and neck region
• Eastern Cooperative Oncology Group Performance Status (ECOGPS) performance status 0 or 1
• Comply with the study protocol
• Capable of signing a written informed consent

Exclusion Criteria:

• An allergy, intolerance, or contraindication to colchicine
• Current treatment with colchicine for medical conditions, e.g. gout and Familial Mediterranean Fever (FMF)
• Estimated glomerular filtration rate (GFR) < 55 ml/min since colchicine should not be given
• Severe liver disease or current aminotransferase levels of more than 1.5 times the upper limit of the normal range
• Previous irradiation to the head and/or neck region
• Distant metastatic disease or locally recurrent disease
• Pre-existing skin rashes, ulcerations, or open wounds in the treatment area
• Known allergic and other systemic skin diseases even when not directly affecting irradiated fields
• Substance abuse, medical conditions, and/or social issues that would limit conduct or follow-up in the research study, in the opinion of the investigator
• Any condition that is unstable or could affect the safety of the patient and their compliance in the study as judged by the investigator
• Using high doses of non-steroidal anti-inflammatory drugs
• Pregnant and lactating women
• Psychiatric illness that would prevent the patient from giving informed consent
• Taking cetuximab or other radiosensitizing agents.

Inclusion Criteria:

1. Histologically or cytologically confirmed metastatic or refractory/recurrent HPV-16+ cancer. 2. Tumor with HPV16 genotype as determined by testing performed in a CLIA certified laboratory. 3. HLA-A*02:01 allele as determined by testing performed in a Clinical Laboratory Improvement Amendments (CLIA) certified laboratory. Participants may be enrolled based on low resolution typing (i.e., HLA-A*02) but the HLA-A*02:01 allele type must be confirmed prior to apheresis. 4. Measurable disease as assessed by RECIST Criteria Version 1.114. 5. Age ≥ 18 years. 6. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 at screening. 7. Must have received prior first line standard therapy or have declined standard therapy. 8. Standard treatment options for first and second-line therapy must be presented and formally declined (Appendix VII). 9. Patients with three or fewer brain metastases that have been treated with surgery or stereotactic radiosurgery are eligible. Lesions that have been treated with stereotactic radiosurgery must be clinically stable for one month before protocol treatment. Patients must be fully recovered from surgery. 10. Negative pregnancy test for women under 55 and all women who have had a menstrual period in the last 12 months. A pregnancy tests is not required for women who have had a bilateral oophorectomy or hysterectomy. 11. Men and women of child-bearing potential must agree to use adequate contraception (i.e., intrauterine device, hormonal barrier method of birth control; abstinence; tubal ligation or vasectomy) prior to study entry and for four months after treatment. Should a women become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately. 12. Seronegative for HIV antibody, hepatitis B antigen, and hepatitis C antibody. If a hepatitis C antibody test is positive, then testing for antigen by RT-PCR for Hepatitis C (HCV) RNA must be negative. 13. Participants must have organ and marrow function as defined below: 1. Leukocytes > 3,000/microliter (mcL) 2. Absolute neutrophil count > 1,500/mcL 3. Platelets > 100,000/mcL 4. Hemoglobin > 8.0 g/dL 5. Total bilirubin within normal institutional limits except in participants with Gilbert's Syndrome who must have a total bilirubin < 3.0 mg/dL. 6. Serum aspartate transferase (AST) (SGOT)/alanine transaminase (ALT) (SGPT) < 2.5 x upper limit of normal (ULN) 7. Calculated creatinine clearance (CrCl) >50 mL/min/1.73 m2for participants with creatinine levels above institutional normal (by the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation). 8. international normalized ratio (INR) or activated partial thromboplastin time ( aPTT) ≤1.5 X ULN unless the subject is receiving anticoagulant therapy. Subjects on anticoagulant therapy must have a PT or aPTT within therapeutic range and no history of severe hemorrhage. 14. More than four weeks must have elapsed since any prior systemic therapy at the time the patient receives the E7 TCR cells. 15. Participants must be able to understand and be willing to sign the written informed consent document. 16. Participants must agree to participate in protocol Cancer Institute of New Jersey (CINJ) 192103 (Pro2021002307) for gene therapy long term follow up and in protocol CINJ 192002 (Pro2021000281) for biospecimen collection study.

Inclusion Criteria:

• STEP 1: Age >= 18 years
• STEP 1: Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
• STEP 1: Patients must have oropharynx cancer (American Joint Committee on Cancer [AJCC] 8) that is p16-positive by immunohistochemistry OR p16 equivocal by IHC and HPV positive by in situ hybridization with the following criteria: >= 10 pack-years, stage T1-2N2-N3 or T3-4N0-3 (less than 10 pack-years is considered a non-smoker) OR < 10 pack-years, stage T4N0-N3 or T1-3N2-3
• STEP 1: Patients must not have known hypersensitivity to nivolumab or compounds of similar chemical or biologic composition.
• STEP 1: Patients with a history of allergic reactions attributed to platinum-based chemotherapy agents are excluded.
• STEP 1: Patients must not have had prior systemic therapy, radiation treatment or surgery for p16 positive oropharyngeal squamous cell carcinoma (OPSCC).
• NOTE: Patients who had resection of T1 or T2 carcinoma with no radiation or chemotherapy are eligible if surgery was done 5 years prior to enrollment
• STEP 1: Patients must not have received previous irradiation for head and neck tumor, skull base, or brain tumors.
• STEP 1: Patients must not receive investigational agents within 4 weeks of enrollment or at any time while on study.
• STEP 1: Patients with evidence of distant metastases or leptomeningeal disease (LMD) are excluded.
• STEP 1: Patients with uncontrolled inter-current illnesses which in the opinion of the investigator will interfere with the ability to undergo therapy including chemotherapy are excluded.
• STEP 1: Patients with a history of prior or second malignancy are excluded, with the exception of curatively treated non-melanoma skin cancer, or curatively treated cervical cancer; additionally, patients curatively treated for malignancy who remain disease-free at > 2 years of follow up, are not excluded.
• STEP 1: Absolute neutrophil count (ANC) >= 1500/mm^3 (must be obtained =< 2 weeks prior to randomization).
• STEP 1: Hemoglobin (Hgb) >= 8.0 g/dL (must be obtained =< 2 weeks prior to randomization).
• STEP 1: Platelet count >= 100,000/mm^3 (must be obtained =< 2 weeks prior to randomization).
• STEP 1: Creatinine clearance of >= 60 ml/min (must be obtained =< 2 weeks prior to randomization). Creatinine clearance may be measured or calculated. If calculating, creatinine clearance, use the Cockcroft-Gault formula.
• STEP 1: Total bilirubin within 1.5 times the normal limits (must be obtained =< 2 weeks prior to randomization).
• STEP 1: Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase [AST]) or serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase [ALT]) within 2.0 times the normal limits (must be obtained =< 2 weeks prior to randomization).
• STEP 1: Alkaline phosphatase within 2.0 times the normal limits (must be obtained =< 2 weeks prior to randomization).
• STEP 1: Patients must not be pregnant or breast-feeding as chemotherapy, radiation, and immunotherapy may have possible teratogenicity effects; in addition, complications from pregnancy may interfere with the ability of patients to have an uninterrupted therapy. All patients of childbearing potential must have a blood test or urine study within 2 weeks prior to randomization to rule out pregnancy. A patient of childbearing potential is any female, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months).
• STEP 1: Patients of childbearing potential must use an accepted and effective method of contraception or abstain from sexual intercourse for at least one week prior to the start of treatment, and continue for 5 months after the last dose of protocol treatment. Patients must also not donate ova during this same time period.
• STEP 1: Patients must have measurable disease
• STEP 1: Patients must have tumor measurements with CT of neck and CT of chest (or CT of neck and FDG PET/CT if standard of care) within 4 weeks prior to Step 1 randomization.
• STEP 1: Patients with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including systemic corticosteroids, should be excluded. These include but are not limited to patients with a history of immune related neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE), connective tissue disease, scleroderma, inflammatory bowel disease (IBD), Crohn's, ulcerative colitis, hepatitis; and patients with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be excluded because of the risk of recurrence or exacerbation of disease. Patients with vitiligo, endocrine deficiencies including thyroiditis managed with replacement hormones including physiologic corticosteroids are eligible. Patients with rheumatoid arthritis and other arthropathies, Sjogren's syndrome and psoriasis controlled with topical medication and patients with positive serology, such as antinuclear antibodies (ANA), anti-thyroid antibodies should be evaluated for the presence of target organ involvement and potential need for systemic treatment but should otherwise be eligible.
• STEP 1: Patients are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger (precipitating event).
• STEP 1: Patients must not have a condition requiring systemic treatment with either corticosteroids (> 10 mg/day prednisone equivalents) or other immunosuppressive medications which are expected to continue during nivolumab administration. Inhaled or topical steroids and adrenal replacement doses > 10 mg/day prednisone equivalents are permitted in the absence of active autoimmune disease
• STEP 1: Patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
• STEP 1: Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
• STEP 1: Patients with a known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) must have no detectable viral load on a stable antiviral regimen
• STEP 1: Patients must not be receiving any other investigational agents.
• STEP 1: Patient must not have a baseline clinically significant hearing loss, which in the opinion of the investigator would preclude the use of cisplatin
• STEP 2: Patients must have progression per RECIST criteria AND tissue-proven progression on Arm B treatment within 12 months after completion of radiation therapy.
• STEP 2: ECOG performance status of 0 or 1.
• STEP 2: Patients must not have known hypersensitivity to nivolumab or compounds of similar chemical or biologic composition.
• STEP 2: Patients must not have received non-protocol anti-cancer therapy after completion of radiation and chemotherapy.
• STEP 2: ANC >= 1500/mm^3 (must be obtained =< 2 weeks prior to registration).
• STEP 2: Hgb >= 8.0 g/dL (must be obtained =< 2 weeks prior to registration).
• STEP 2: Platelet count >= 100,000/mm^3 (must be obtained =< 2 weeks prior to registration).
• STEP 2: Creatinine within institutional limits of normal (must be obtained =< 2 weeks prior to registration)
• STEP 2: Total bilirubin within 1.5 times the normal limits (must be obtained =< 2 weeks prior to registration).
• STEP 2: SGOT (AST) or SGPT (ALT) within 2.0 times the normal limits (must be obtained =< 2 weeks prior to registration).
• STEP 2: Alkaline phosphatase within 1.5 times the normal limits (must be obtained =< 2 weeks prior to registration).
• STEP 2: Patients must not be pregnant or breast-feeding as chemotherapy, radiation, and immunotherapy may have possible teratogenicity effects; in addition, complications from pregnancy may interfere with the ability of patients to have an uninterrupted therapy. All women of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy. A women of childbearing potential is any female, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months).
• STEP 2: Patients of childbearing potential must use an accepted and effective method of contraception or abstain from sexual intercourse for at least one week prior to the start of treatment, and continue for 5 months after the last dose of protocol treatment. Patients must also not donate ova during this same time period.
• STEP 2: Patients must have measurable disease at the time of documented progression
• NOTE: For patients that have undergone salvage surgery for disease recurrence, measurable disease is not required at the time of registration to Step 2
• STEP 2: Patients must have tumor measurements with CT of neck and CT of chest (or CT of neck and FDG PET/CT if standard of care) within 4 weeks prior to Step 2 registration
• NOTE: Patients that have undergone salvage surgery for disease recurrence prior to Step 2 are not required to have measurable disease post-resection, but must have CT of neck and CT of chest (or CT of neck and FDG PET/CT if standard of care) after salvage surgery and within 4 weeks prior to step 2 registration to establish a baseline prior to nivolumab

Inclusion Criteria:

• Has histologically confirmed new diagnosis of resectable, non-metastatic, squamous cell carcinoma that is either: Stage III Human Papillomavirus (HPV) positive oropharyngeal primary that is tumor size (T) 4, lymph node involvement (N) 0-2, no distant metastases (M0); Stage III or IVA oropharyngeal HPV negative; or Stage III or IVA larynx/hypopharynx/oral cavity primaries.
• Is eligible for primary surgery based on investigator decision and per local practice
• Female and male participants of reproductive potential must agree to use adequate contraception throughout the study period and for up to 180 days after the last dose of study therapy.
• Male participants must refrain from donating sperm throughout the study period and for up to 180 days after the last dose of study therapy
• Female participant that is not pregnant or breastfeeding
• Has evaluable tumor burden (measurable and/or non-measurable tumor lesions) assessed by computed tomography (CT) scan or magnetic resonance imaging (MRI), based on RECIST version 1.1
• Has provided newly obtained core or excisional biopsy of a tumor lesion not previously irradiated
• Has results from testing of HPV status for oropharyngeal cancer defined as p16
• Has Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 performed within 10 days of randomization

Exclusion Criteria:

• Has Stage T4B and/or N3 LA HNSCC and/or distant metastases
• Has cancer outside of the oropharynx, larynx, and hypopharynx or oral cavity. such as nasopharyngeal, sinus, other para-nasal, or other unknown primary head and neck cancer (HNC)
• Female participant who has a positive urine pregnancy test within 72 hours prior to study start or within 24 hours prior to the start of radiotherapy with or without cisplatin.
• Has received prior therapy with an anti-programmed cell death receptor 1(PD-1), anti-programmed cell death receptor ligand 1(PD-L1), or anti-programmed cell death receptor ligand 2 (PD-L2) agent or with an agent directed to another co-inhibitory T-cell receptor
• Has received prior radiotherapy treatment or systemic anti-cancer therapy including investigational agents for the HNC under study prior to study start
• Has received a live vaccine within 30 days prior to randomization
• Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to randomization
• Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to randomization
• Has a known additional malignancy that is progressing or has required active treatment within the past 3 years with the exception of basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g. in situ cervical cancer or breast carcinoma) that have undergone potentially curative therapy
• Has radiographically detectable (even if asymptomatic and/or previously treated) central nervous system metastases and/or carcinomatous meningitis
• Has Grade ≥2 audiometric hearing loss
• Has Grade ≥2 neuropathy
• Has Grade 3-4 bleeding due to the underlying malignancy
• Has received major surgery or has not recovered adequately from the toxicity and/or complications from the intervention prior to study start
• Has had previous allogeneic tissue/solid organ transplant
• Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients, radiotherapy, cisplatin or their analogs
• Has an active autoimmune disease that has required systemic treatment in past 2 years
• Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis
• Has an active infection requiring systemic therapy
• Has a known history of human immunodeficiency virus (HIV) infection
• Has a known history of or is positive for Hepatitis B (defined as hepatitis B surface antigen [HBsAg] reactive) or known active Hepatitis C (defined as Hepatitis C virus [HCV] ribonucleic acid is detected).
• Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the participant's participation for the full duration of the study, or is not in the best interest of the participant to participate, in the opinion of the investigator
• Has a known psychiatric or substance abuse disorder that would interfere with the participant's ability to cooperate with the requirements of the study

Inclusion Criteria:

• age > 18 years;
• Diagnosed with a first primary invasive oral or oropharyngeal cancer between 1 and 3 years ago;
• Currently cancer free (but can have experienced a recurrence);
• Has internet access;
• Read English;
• Has sufficient vision to read a survey and complete an online intervention

Exclusion Criteria:

Inclusion Criteria:

• Patients must have pathologically confirmed HNSCC (including tumors of the oropharynx, hypopharynx, larynx, oral cavity, nasal cavity, maxillary and other paranasal sinuses, and unknown primary of the head and neck), with measurable disease as per RECIST 1.1
• Oropharyngeal and unknown primary squamous cell cancers must test for human papilloma virus (HPV), for example by p16 immunohistochemistry (IHC), in situ hybridization (ISH), or polymerase chain reaction (PCR). HPV testing is not required for other HNSCC primary tumor sites
• For the dose escalation phase only (not the expansion phase), patients with p16-positive tumors are eligible if clinical stage III (cT4 or cN3, M0) according to the American Joint Committee on Cancer (AJCC)/TNM Staging System, 8th edition (Ed.)
• For both the dose escalation and expansion phases, patients with p16-negative (or not tested) tumors are eligible if clinical stage III-IVB (locally advanced but non-metastatic) according to the AJCC/TNM Staging System, 8th Ed.
• Clinical stage III-IVB (locally advanced but non-metastatic) according to the American Joint Committee on Cancer (AJCC)/TNM Staging System, 8th Ed.
• Must be candidate for concurrent, definitive cisplatin and radiation therapy as judged by the treating physician
• Able to swallow tablets at the time of enrollment
• Age >= 18 years. Because no dosing or adverse event data are currently available on the use of ipatasertib in combination with chemoradiation in patients < 18 years of age, children are excluded from this study
• Eastern Cooperative Oncology Group (ECOG) performance status 0-1
• Life expectancy of greater than 3 months
• Absolute neutrophil count >= 1500/mcL
• Hemoglobin >= 9 g/dL
• Platelets >= 100,000/mcL
• Serum albumin >= 3 g/dL
• Total bilirubin =< 1.5 x institutional upper limit of normal (ULN)
• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x institutional ULN / 2 x institutional ULN
• Alkaline phosphatase (ALP) =< 2.0 x institutional ULN
• Partial thromboplastin time (PTT) (or activated [a]PTT) and international normalized ratio (INR) =< 1.5 institutional ULN (except for patients receiving anticoagulation therapy)
• Creatinine clearance (CLcr) > 50 mL/min
• For this calculation, use the Cockroft-Gault formula
• Fasting glucose =< 150 mg/dL (8.3 mmol/L) and glycosylated hemoglobin (HbA1c ) =< 7.5% (58 mmol/mol)
• Human immunodeficiency virus (HIV)-infected patients are eligible if on effective anti-retroviral therapy with undetectable viral load within 6 months
• Patients with past hepatitis B virus (HBV) infection or resolved HBV infection (defined as having a negative hepatitis B virus surface antigen [HBsAg] test and a positive hepatitis B core antibody [HBcAb] test, accompanied by a negative HBV deoxyribonucleic acid [DNA] test) are eligible. Patients with chronic HBV infection are eligible if the HBV viral load is undetectable on suppressive therapy, if indicated. Patients undergoing current treatment with anti-viral therapy for HBV are ineligible
• Patients with a history of hepatitis C virus (HCV) infection are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA). Patients with HCV infection who are currently on treatment are eligible if they have an undetectable HCV viral load
• Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial
• The effects of ipatasertib on the developing human fetus are unknown. For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods with a failure rate of < 1% per year during the treatment period and for at least 28 days after the last dose of ipatasertib and agreement to refrain from donating eggs during this same period. For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm during the treatment period and for 28 days after the last dose of ipatasertib
• Ability to understand and the willingness to sign a written informed consent document
• For the expansion cohort only, patients must agree to undergo mandatory on-treatment biopsies, and have tumors amenable to on-treatment biopsies. This is not applicable to the dose escalation cohort where no on-treatment biopsies are obtained

Exclusion Criteria:

• Primary tumor of nasopharynx, salivary, thyroid or parathyroid glands, or skin
• Distant metastases from the current HNSCC
• Prior treatment (e.g., chemotherapy, radiation, or definitive surgery) for the current locally advanced HNSCC is not permitted. Biopsies, including those performed under anesthesia, are not considered surgery. Patients who underwent prior definitive surgery alone for an early stage (T1-2N0) HNSCC which has now recurred with stage III-IVB disease at least 3 months after the initial surgery are eligible
• For patients with a prior history of another malignancy, no prior chemotherapy or radiation may have been administered within 6 weeks prior to study entry. Among patients who received prior radiation to the head and neck or adjacent anatomical site for another malignancy, there may be no overlap with current area to be irradiated
• Current use of any other investigational agents
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to ipatasertib or other agents used in study
• Treatment with strong inhibitors or inducers of CYP3A4 or P-glycoprotein within 2 weeks or 5 drug-elimination half-lives, whichever is longer, prior to initiation of study drug. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product
• Patients with uncontrolled intercurrent illness, including active infection
• Pregnant women are excluded from this study because ipatasertib is an oral AKT inhibitor with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with ipatasertib, breastfeeding should be discontinued if the mother is treated with ipatasertib. These potential risks may also apply to other agents used in this study
• Patients with Type I or Type II diabetes mellitus requiring insulin at study entry. Patients with non-insulin dependent Type II diabetes mellitus are eligible, as are patients who are on a stable dose of oral diabetes medication >= 4 weeks prior to initiation of study treatment. Patients must meet the laboratory eligibility criteria for fasting blood glucose and hemoglobin A1c
• History of or active inflammatory bowel disease (e.g., Crohn's disease and ulcerative colitis) or active bowel inflammation (e.g., diverticulitis)
• History of malabsorption syndrome or other condition that would interfere with enteral absorption or results in the inability or unwillingness to swallow pills
• Lung disease: pneumonitis, interstitial lung disease, idiopathic pulmonary fibrosis, cystic fibrosis, aspergillosis, active tuberculosis, or history of opportunistic infections (pneumocystis pneumonia or cytomegalovirus pneumonia)
• Known clinically significant history of liver disease consistent with Child Pugh Class B or C, including active viral or other hepatitis (e.g., positive for hepatitis B surface antigen [HBsAg] or hepatitis C virus [HCV] antibody at screening), or cirrhosis.
• Grade >= 2 uncontrolled or untreated hypercholesterolemia (cholesterol > 300 mg/dL or > 7.75 mmol/L) or hypertriglyceridemia (triglycerides > 300 mg/dL or > 3.42 mmol/L)

Inclusion Criteria:

• Biopsy proven (from primary lesion and/or lymph nodes) diagnosis of cancer of the nasopharynx
• Sites are required to complete Step 1 registration before submitting specimens for EBV DNA analysis.
• Patients must have detectable pretreatment plasma EBV DNA, determined by the central lab prior to Step 2 registration (see Section 10.2 for details of specimen submission).
• For patients who have detectable plasma EBV DNA tested at one of the credentialed central labs (listed on the EBV DNA Testing Specimen Transmittal form) within 28 days prior to Step 1 registration: that test result can be used for eligibility without the need for re-testing. To use this test result for eligibility, the central lab must enter the test result through the pathology portal, and the site must follow the instructions in Section 5.4.
• Stage II-IVB disease (AJCC, 7th ed.) with no evidence of distant metastasis, based upon the following minimum diagnostic workup:
• History/physical examination by a Medical Oncologist or Clinical Oncologist or Radiation Oncologist or ENT, which must include an endoscopic evaluation, a complete list of current medications, and assessment of weight and weight loss in the past 6 months within 21 days prior to registration;
• Evaluation of tumor extent required within 28 days prior to registration:
• MRI of the nasopharynx and neck; or CT of the nasopharynx and neck with ≤ 3 mm contiguous slices with contrast and bone windows (to evaluate base of skull involvement). Note: If a treatment planning CT scan is used, it must be with ≤ 3 mm contiguous slices with contrast and be read by a radiologist. Please refer to section 6.3.2 for MRI requirement for target delineation.
• To rule out distant metastasis, patients must undergo the following imaging within 28 days prior to registration: 1. a CT scan with contrast of the chest and abdomen (required), and the pelvis (optional), or a total body PET/CT scan (non-contrast PET/CT is acceptable); 2. a bone scan only when there is suspicion of bone metastases (a PET/CT scan can substitute for the bone scan).
• Zubrod performance status 0-1 within 21 days prior to registration
• Absolute neutrophil count (ANC) ≥ 1,500 cells/mm^3
• Platelets ≥ 100,000 cells/mm^3
• Hemoglobin ≥ 8.0 g/dl (Note: the use of transfusion or other intervention to achieve hemoglobin [Hgb] ≥ 8.0 g/dl is acceptable)
• Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN)
• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 1.5 x institutional ULN
• Alkaline phosphatase ≤ 1.5 x institutional ULN
• Serum creatinine ≤ 1.5 mg/dl or calculated creatinine clearance (CC) ≥ 50 ml/min determined by 24-hour urine collection or estimated by Cockcroft-Gault formula
• Negative serum pregnancy test within 14 days prior to registration for women of childbearing potential
• Women of childbearing potential and male participants who are sexually active must agree to use a medically effective means of birth control throughout protocol treatment
• Patient must provide study specific informed consent prior to study entry, including the mandatory pre-treatment plasma EBV DNA assay

Exclusion Criteria:

• Prior invasive malignancy (except node negative, non-melanomatous skin cancer) unless disease free for a minimum of 1095 days (3 years) (for example, carcinoma in situ of the breast, oral cavity, or cervix are all permissible)
• Prior systemic chemotherapy for the study cancer; note that prior chemotherapy for a different cancer is allowable; however, at least 6-weeks recovery is necessary if the last regimen included nitrosourea or mitomycin
• Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields
• Patients with hearing loss assessed to be primarily sensorineural in nature, requiring a hearing aid, or intervention (i.e. interfering in a clinically significant way with activities of daily living); a conductive hearing loss that is tumor-related is allowed
• ≥ Grade 2 peripheral sensory neuropathy (CTCAE, v. 4.0)
• Severe, active co-morbidity, defined as follows:
• Major medical or psychiatric illness, which in the investigator's opinion would interfere with the completion of therapy and follow up or with full understanding of the risks and potential complications of the therapy
• Unstable angina and/or uncontrolled congestive heart failure within the past 6 months
• Myocardial infarction within the last 6 months
• Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration; note that patients switched from IV antibiotics and currently on oral antibiotics whose infection is assessed to be adequately treated or controlled are eligible
• Chronic Obstructive Pulmonary Disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy within 30 days prior to registration
• Acquired Immune Deficiency Syndrome (AIDS) based upon current Centers for Disease Control and Prevention (CDC) definition; note, however, that Human Immunodeficiency Virus (HIV) testing is not required for entry into this protocol. The need to exclude patients with AIDS from this protocol is necessary because the treatments involved in this protocol may be significantly immunosuppressive.
• Pregnancy or women of childbearing potential and men who are sexually active and not willing/able to use medically acceptable forms of contraception
• Prior allergic reaction to the study drug(s) involved in this protocol
• Patients with undetectable pre-treatment plasma EBV DNA

Inclusion Criteria:

• PRIOR TO STEP 1 REGISTRATION INCLUSION:
• Pathologically (histologically or cytologically) proven diagnosis of squamous cell carcinoma of the oral cavity, including the oral (mobile) tongue, floor of mouth (FOM), mucosal lip, buccal mucosa, lower alveolar ridge, upper alveolar ridge, retromolar gingiva (retromolar trigone; RMT), or hard palate prior to registration
• Appropriate stage for study entry (T1-2N0M0; American Joint Committee on Cancer [AJCC] 8th edition [ed.]) based on the following diagnostic workup:
• History/physical examination within 42 days prior to registration
• Imaging of head and neck within 42 days prior to registration
• PET/CT scan or contrast neck CT scan, or gadolinium-enhanced neck magnetic resonance imaging (MRI) or lateral and central neck ultrasound; diagnostic quality CT is preferred and highly recommended for the PET/CT when possible.
• Imaging of chest within 42 days prior to registration; chest x-ray, CT chest scan (with or without contrast) or PET/CT (with or without contrast)
• Surgical assessment within 42 days prior to registration. Patient must be a candidate for surgical intervention with sentinel lymph node (SLN) biopsy and potential completion neck dissection (CND) or elective neck dissection (END)
• Surgical resection of the primary tumor will occur through a transoral approach with anticipation of resection free margins
• Zubrod performance status 0-2 within 42 days prior to registration
• For women of child-bearing potential, negative serum or urine pregnancy test within 42 days prior to registration
• The patient or a legally authorized representative must provide study-specific informed consent prior to study entry
• Only patients who are able to read and understand English are eligible to participate as the mandatory patient reported NDII tool is only available in this language
• PRIOR TO STEP 2 RANDOMIZATION:
• FDG PET/CT required prior to step 2. Note: FDG PET/CT done prior to step 1 can be submitted for central review.
• PET/CT node negative patients, determined by central read, will proceed to randomization.
• PET/CT node positive patients will go off study, but will be entered in a registry and data will be collected to record the pathological outcome of neck nodes for diagnostic imaging assessment and future clinical trial development
• NOTE: All FDG PET/CT scans must be performed on an American College of Radiology (ACR) accredited scanner (or similar accrediting organization)
• The patient must complete NDII prior to step 2 registration

Exclusion Criteria:

• PRIOR TO STEP 1 REGISTRATION EXCLUSION:
• Definitive clinical or radiologic evidence of regional (cervical) and/or distant metastatic disease
• Prior non-head and neck invasive malignancy (except non-melanomatous skin cancer, including effectively treated basal cell or squamous cell skin cancer, or carcinoma in situ of the breast or cervix) unless disease free for ≥ 2 years
• Diagnosis of head and neck squamous cell carcinoma (SCC) in the oropharynx, nasopharynx, hypopharynx, and larynx
• Unable or unwilling to complete NDII (baseline only)
• Prior systemic chemotherapy for the study cancer; note that prior chemotherapy for a different cancer is allowable
• Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields
• Patient with severe, active co-morbidity that would preclude an elective or completion neck dissection
• Pregnancy and breast-feeding mothers
• Incomplete resection of oral cavity lesion with a positive margin; however, an excisional biopsy is permitted
• Prior surgery involving the lateral neck, including neck dissection or gross injury to the neck that would preclude surgical dissection for this trial. Prior thyroid and central neck surgery is permissible; biopsy is permitted. Note: Borderline suspicious nodes that are ≥ 1 cm with radiographic finding suggestive of NOT malignant should be biopsied using ultrasound-guided (U/S-guided) fine-needle aspiration (FNA) biopsy
• Underlying or documented history of hematologic malignancy (e.g., chronic lymphocytic leukemia [CLL]) or other active disease capable of causing lymphadenopathy (sarcoidosis or untreated mycobacterial infection)
• Actively receiving systemic cytotoxic chemotherapy, immunosuppressive, anti-monocyte or immunomodulatory therapy
• Currently participating in another investigational therapeutic trial

Inclusion Criteria:

• Histologically proven squamous cell carcinoma of the oropharynx
• Clinical stage T1-2, N0-N3, M0 by American Joint Committee on Cancer (AJCC) 8 criteria
• Must have tumors deemed surgically resectable with acceptable morbidity
• Estimated life expectancy of at least 12 weeks
• Must give informed consent
• Must have Eastern Cooperative Oncology Group (ECOG) performance status =< 3
• Must have detectable circulating HPV DNA levels
• Platelets >= 100,000/ul
• Absolute neutrophil count (ANC) >= 1,500/ul
• Hemoglobin > 8 g/dl (use of transfusion to achieve this is acceptable)
• Total bilirubin < 2 X institutional upper limit of normal (ULN)
• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) < 3 X institutional ULN
• Serum creatinine < 2 x institutional ULN or creatinine clearance > 50 ml/min as determined by 24 hour collection or estimated by Cockcroft-Gault formula
• Negative pregnancy test, if applicable

Exclusion Criteria:

• Patients may not have received previous therapy for their head and neck squamous cell carcinoma (SCC), including chemotherapy, radiation therapy, or surgery beyond biopsy
• Second primary malignancy. Exceptions are:
• Patient had a second primary malignancy but has been treated and disease free for at least 3 years
• In situ carcinoma (e.g. in situ carcinoma of the cervix)
• Non-melanomatous carcinoma of the skin
• Patients with metastatic disease beyond the neck will be excluded
• Serious concomitant systemic disorders (including active infections) that would compromise the safety of the patient or compromise the patient's ability to complete the study, at the discretion of the investigator
• Age < 18 years
• Patients with human immunodeficiency virus (HIV) infection are not automatically excluded, but must meet the following criteria: CD4 count is > 499/cu mm and their viral load is < 50 copies/ml. Use of highly active antiretroviral therapy (HAART) is allowed
• Grade 3-4 electrolyte abnormalities (Common Terminology Criteria for Adverse Events [CTCAE], version [v.] 5)
• Serum calcium (ionized or adjusted for albumin) < 7 mg/dl (1.75 mmol/L) or > 12.5 mg/dl (> 3.1 mmol/L) despite intervention to normalize levels
• Magnesium < 0.9 mg/dl (< 0.4 mmol/L) or > 3 mg/dl (> 1.23 mmol/L) despite intervention to normalize levels
• Potassium < 3.0 mmol/L or > 6 mmol/L despite intervention to normalize levels
• Sodium < 130 mmol/L or > 155 mmol/L despite intervention to normalize levels
• Women who are pregnant, due to the teratogenic effects of radiation therapy and chemotherapy on the unborn fetus. Women of childbearing age must agree to undergo a pregnancy test prior to therapy and to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation and for 6 months after. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately
• Tumor deemed unresectable with acceptable morbidity:
• Tumors > 4 cm in size (T3 or higher)
• Tumors of the base of tongue < 4 cm but with deep invasion of tongue musculature placing hypoglossal nerve or both lingual arteries at risk
• Significant extension into hypopharynx
• Extension into soft palate beyond 1/3 of the width
• Clinically extensive extranodal extension (ENE) e.g. radiologic evidence of invasion of carotid artery, gross extension into sternocleidomastoid muscle or deep neck muscles. Lymph nodes larger than 6 cm without clinical ENE will be allowed