Key Inclusion Criteria:

1. Have documented CD20+ aggressive B-NHL, with disease that has progressed after at least 2 lines of systemic therapy containing an anti-CD20 antibody and an alkylating agent. 2. Measurable disease on cross sectional imaging as defined in the protocol 3. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 4. Adequate bone marrow, renal and hepatic function as defined in the protocol 5. During dose expansion phase of the study, participant should be willing to undergo mandatory tumor biopsies, if in the opinion of the investigator, the participant has an accessible lesion that can be biopsied without significant risk to the participant.

Key Exclusion Criteria:

1. Prior treatments with allogeneic stem cell transplantation or solid organ transplantation, treatment with anti-CD20 x anti- CD3 bispecific antibody, such as odronextamab 2. Diagnosis of mantle cell lymphoma (MCL) 3. Primary central nervous system (CNS) lymphoma or known involvement by non-primary CNS lymphoma 4. Treatment with any systemic anti-lymphoma therapy within 5 half-lives or within 14 days prior to first administration of study drug, whichever is shorter 5. Standard radiotherapy within 14 days of first administration of study drug. 6. Continuous systemic corticosteroid treatment with more than 10 mg per day of prednisone or corticosteroid equivalent within 72 hours of start of odronextamab 7. Co-morbid conditions, as described in the protocol 8. Infections, as described in the protocol 9. Allergy/hypersensitivity: Known hypersensitivity to both allopurinol and rasburicase NOTE: Other protocol defined inclusion / exclusion criteria apply

Key Inclusion Criteria

• Participant must be greater than or equal to (>=) 18 years of age, at the time of signing informed consent
• All participants must have relapsed or refractory disease for each histologic subtype
• Mature aggressive large B cell NHL and Follicular Lymphoma Grade 3b: Participants must have >= 2 lines of systemic therapy or >=1 line of systemic therapy in case of participants ineligible for high-dose chemotherapy and autologous Hematopoietic stem cell transplantation (HSCT). Participants also must have had exposure to an anthracycline and an anti-CD20 targeted agent
• Follicular lymphoma Grade 1-3a and Marginal Zone Lymphoma: Participants must have >=2 prior lines of anti-neoplastic systemic therapy. Participants also must have prior exposure to an anti-CD20 monoclonal antibody
• Tumor must be cluster of differentiation (CD) 20 positive
• Measurable disease as defined by Lugano 2014 classification
• Eastern Cooperative Oncology Group (ECOG) performance status of either 0 or 1

Key Exclusion Criteria

• Diagnosis of Human herpes virus (HHV) 8-positive Diffuse large B Cell lymphoma (DLBCL)
• Prior allogeneic Hematopoietic stem cell transplantation (HSCT)
• Autologous stem cell transplant within 12 weeks of chimeric antigen receptor (CAR) T cell infusion
• Uncontrolled active infections
• History of deep vein thrombosis or pulmonary embolism within six months of infusion (except for line associated deep vein thrombosis [DVT])
• History of stroke, unstable angina, myocardial infarction, congestive heart failure ( New York Heart Association [NYHA] Class III or IV), severe cardiomyopathy or ventricular arrhythmia requiring medication or mechanical control within 6 months of screening
• History of a seizure disorder, cerebrovascular ischemia/hemorrhage, dementia, cerebellar disease or neurodegenerative disorder
• Known history or prior diagnosis of optic neuritis or other immunologic or inflammatory disease affecting the central nervous system
• Active central nervous system (CNS) involvement by malignancy
• Current active liver or biliary disease (except for Gilbert's syndrome or asymptomatic gallstones)

• Participant must be greater than or equal to (>=) 18 years of age, at the time of signing informed consent
• Diagnosis of mature aggressive large B cell non-Hodgkin lymphoma or follicular lymphoma
• Tumor must be histologically confirmed cluster of differentiation (CD)19 and/or CD20 positive
• Must have relapsed or refractory disease with the following indications for each histologic subtype: Mature aggressive large B cell non-Hodgkin lymphoma (NHL) and follicular lymphoma Grade 3b: Participants must have >= 2 lines of systemic therapy, or >= 1 line of systemic therapy for participants who are ineligible for autologous stem cell transplant; Follicular lymphoma Grade 1-3a and marginal zone lymphoma: Participants must have >= 2 prior lines of anti-neoplastic systemic therapy. Participants also must have prior exposure to an anti-CD20 monoclonal antibody
• Measurable disease as defined by Lugano 2014 classification
• Eastern cooperative oncology group (ECOG) performance status of either 0 or 1

Exclusion Criteria

• Diagnosis of Human herpes virus (HHV) 8-positive diffuse large B Cell lymphoma (DLBCL)
• Prior allogeneic hematopoietic stem cell transplantation (HSCT)
• Autologous stem cell transplant within 12 weeks of chimeric antigen receptor (CAR) T cell infusion
• Uncontrolled active infections
• History of deep vein thrombosis or pulmonary embolism within six months of infusion (except for line associated deep vein thrombosis [DVT])
• History of stroke, unstable angina, myocardial infarction, congestive heart failure New York Heart Association (NYHA) Class III or IV, severe cardiomyopathy or ventricular arrhythmia requiring medication or mechanical control within 6 months of screening
• History of a seizure disorder, cerebrovascular ischemia/hemorrhage, dementia, cerebellar disease or neurodegenerative disorder
• Known history or prior diagnosis of optic neuritis or other immunologic or inflammatory disease affecting the central nervous system
• Current active liver or biliary disease (except for Gilbert's syndrome or asymptomatic gallstones)

Inclusion Criteria:

• Men and women, age ≥18 and ≤75 years
• Pathologically confirmed DLBCL, sufficient diagnostic material should be available to forward to a central laboratory for gene expression profiling and pathology review.
• No prior treatment for DLBCL
• Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2.
• International Prognostic Index (IPI) score of 1 to 5
• Disease Stage II to IV by the Ann Arbor Classification
• Adequate organ and marrow function
• Agreement to use highly effective forms of contraception during the study and 12 months after the last dose of rituximab

Exclusion Criteria:

• Evidence of severe or uncontrolled systemic diseases
• Known history of a bleeding diathesis (i.e., haemophilia, von Willebrand disease)
• History of stroke or intracranial haemorrhage in preceding 6 months.
• Known CNS lymphoma or leptomeningeal disease
• Known primary mediastinal lymphoma
• Known High-grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements
• Prior history of indolent lymphoma or CLL
• History of or ongoing confirmed PML
• Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of first dose of study drug, or any Class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification
• Malabsorption syndrome, disease significantly affecting gastrointestinal function, resection of the stomach, extensive small bowel resection that is likely to affect absorption, symptomatic inflammatory bowel disease, partial or complete bowel obstruction, or gastric restrictions and bariatric surgery, such as gastric bypass.
• Uncontrolled active systemic fungal, bacterial, viral, or other infection
• Prior anthracycline use ≥150 mg/m2

Inclusion Criteria:

• Participants must have histologically or cytologically confirmed diffuse large B-cell lymphoma (DLBCL), Ann Arbor Stage IIX (bulky), III or IV. Participants with DLBCL transformed from follicular lymphoma (FL) or marginal zone lymphoma (MZL, including mucosa-associated lymphoid tissue [MALT] lymphomas), lymphoplasmacytic lymphoma (LPL), or nodular lymphocyte-predominant Hodgkin Lymphoma (NLPHL) are eligible. Participants with Grade IIIB follicular lymphoma (FL) or high-grade B-cell lymphomas with MYC and BCL2 and/or BCL6 rearrangements are also eligible. Participants with DLBCL that arose from prior CLL (Richter's transformation) are not eligible.
• As defined by the World Health Organization (WHO), eligible lymphoma subtypes include the following:
• DLBCL, not otherwise specified (NOS)
• DLBCL, germinal-center B-cell type (GCB)
• DLBCL, activated B-cell type (ABC)
• T-cell histiocyte-rich B-cell lymphomas (THRBCL)
• Primary cutaneous DLBCL, leg type
• Intravascular large B cell lymphoma
• EBV+ DLBCL, NOS
• DLBCL associated with chronic inflammation
• HHV8+ DLBCL, NOS
• High-grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements
• High grade B-cell lymphoma, NOS
• Follicular lymphoma grade 3b
• Participants must have staging imaging performed within 28 days prior to registration, as follows. Positron emission tomography (PET)-computed tomography (CT) baseline scans are strongly preferred; diagnostic quality magnetic resonance imaging (MRI), contrast-enhanced CT, or contrast-enhanced MRI scans are also acceptable if PET-CT is not feasible at baseline. Note: PET-CT will be required at end of treatment (EOT) and progression for response assessment. All measurable lesions (longest diameter >= 1.5 cm) must be assessed within 28 days prior to registration. Tests to assess non-measurable disease must be performed within 42 days prior to registration.
• Participants with known human immunodeficiency virus (HIV)-infection are eligible providing they are on effective anti-retroviral therapy and have undetectable viral load at their most recent viral load test (must be within 26 weeks prior to registration). Participants with known HIV must have a CD4 count checked within 28 days prior to registration, but may proceed with therapy regardless of CD4 count.
• All participants must be screened for chronic hepatitis B virus (HBV) within 28 days prior to registration. Participants with known HBV infection (positive serology) must also have a HBV viral load performed within 28 days prior to registration, and participants must have an undetectable HBV viral load on suppressive therapy within 28 days prior to registration. Participants found to be HBV carriers during screening are eligible and must receive standard of care prophylaxis. Participants with active hepatitis B (HBV viral load > 500 IU/mL) within 28 days prior to registration are not eligible
• Participants with a known history of hepatitis C virus (HCV) infection must have an undetectable HCV viral load within in 28 days prior to registration
• Participants must have a Zubrod performance status of 0-2
• Participants must have adequate renal function, as demonstrated by a creatinine clearance, calculated by the Cockcroft and Gault formula, of >= 30 ml/min that was obtained within 28 days prior to registration
• Aspartate aminotransferase (AST) =< 2.5 x institutional upper limit of normal (IULN), alanine aminotransferase (ALT) =< 2.5 x IULN (within 28 days prior to registration)
• Total bilirubin =< 2 x institutional upper limit of normal (IULN), unless due to Gilbert's disease, hemolysis, or lymphomatous involvement of liver (within 28 days prior to registration). Note: If total bilirubin is elevated, and direct bilirubin is subsequently performed (within 28 days prior to registration) and resulted to be =< 2 x IULN, the participant will be considered eligible
• Absolute neutrophil count (ANC) >= 1000/mcL (within 28 days prior to registration)
• Platelets >= 75,000/mcL (within 28 days prior to registration)
• Hemoglobin (Hgb) >= 8 g/ dL (within 28 days prior to registration)
• If there is a documented lymphomatous involvement of the bone marrow, bone marrow function within 28 days prior to registration, as evidenced by:
• ANC >= 500/mcL
• Platelets >= 50,000/mcL
• Hemoglobin (Hgb) >= 8 g/ dL
• Participants must have a left ventricular ejection (LVEF) fraction >= 45% as measured by echocardiogram or radionuclide (multigated acquisition scan [MUGA]) ventriculography within 56 days prior to registration
• For the duration of the study treatment period and for at least 4 months following the last dose of study drug, male participants must agree to use effective contraceptive methods during sexual contact with a female of childbearing potential (FCBP) and must agree to refrain from semen or sperm donation during the same timeframe. Effective contraceptive methods include a history of vasectomy, use of hormonal contraception or an intrauterine device (IUD) by the female partner, or use of condoms
• A FCBP is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months)

Exclusion Criteria:

• Participants must not have known lymphomatous involvement of the central nervous system (CNS)
• Participants must not have active inflammatory bowel disease (such as, Crohn's disease, ulcerative colitis), celiac disease (i.e., sprue), prior gastrectomy or upper bowel removal, or any other gastrointestinal disorder or defect that would interfere with the absorption, distribution, metabolism, or excretion of the study drug and/or predispose the subject to an increased risk of gastrointestinal toxicity
• Participants must not have received any prior cytotoxic chemotherapy or rituximab for treatment of the newly diagnosed DLBCL except for the pre-phase treatment (within specified dose range) that may have either started before or may start after registration to S1918. Inhaled, nasal, and topical steroid use is allowed. Prior cytotoxic chemotherapy and/or antibody therapy for an indolent lymphoma prior to transformation is allowed. Up to 4 doses of intrathecal (IT) chemotherapy administered for central nervous system (CNS) prophylaxis is allowed in addition to protocol therapy. High-dose intravenous methotrexate is not allowed.
• Participants must not have received more than a cumulative of dose 250 mg/m^2 of prior doxorubicin (or equivalent dose of another anthracycline, such as epirubicin) therapy (at any time prior to registration).
• Participants must not currently be receiving any other investigational agents
• Participant must not have a history of allergic reactions attributed to azacitidine, mannitol, or other hypomethylating agents
• Participants must not have active infection (systemic fungal, bacterial, or viral infection) that is not controlled (defined as ongoing signs/symptoms related the infection without improvement despite appropriate antibiotics, antiviral therapy, and/or other treatment)
• Participants must not have active cardiac disease within 26 weeks prior to registration, including: symptomatic congestive heart failure (New York Heart Association [NYHA] class 4), unstable angina pectoris, hemodynamically unstable cardiac arrhythmia, or myocardial infarction
• Participants must not have >= grade 2 neuropathy, by Common Terminology Criteria for Adverse Events (CTCAE) version (v.) 5.0, within 28 days prior to registration
• Participants must not have any other known uncontrolled intercurrent illness including, but not limited to ongoing psychiatric illness/social situations that would limit compliance with study requirements

Inclusion Criteria:

• INCLUSION CRITERIA FOR SCREENING (STEP 0 - PREREGISTRATION)
• Patients must have histologically confirmed mantle cell lymphoma, with cyclin D1 by immunohistochemical stains and/or t(11;14) by cytogenetics or FISH. If patient has cyclin D1 negative mantle cell lymphoma with classical morphology and an expression profile (including SOX11+) that is otherwise indistinguishable from mantle cell lymphoma, communication with investigator is required for consideration of enrollment. The proliferation rate, using Ki-67 or MIB-1, should also be determined, but is not required until Step 1 registration. Patients may register to Step 0 without a documented Ki-67 index.
• Patients should be deemed to be potentially eligible and willing candidates for auto-HCT by the enrolling physician
• Patient may be receiving or have completed induction therapy within 60 days prior to preregistration to step 0; no more than 300 days may have passed between the first day of induction therapy and preregistration to step 0
• For patients who have completed induction therapy, restaging evaluation must show status of partial (PR) or complete response (CR); patients preregistered post-induction with evidence of clinical disease progression are not eligible for preregistration
• Up to two regimens of chemotherapy are allowed as long as a continuous response was ongoing throughout therapy
• NOTE: For example, a patient who started treatment with rituximab/bendamustine and was then switched to rituximab(R)-cyclophosphamide, doxorubicin hydrochloride, vincristine sulfate, and prednisone (CHOP) (due to insufficient response or excessive toxicity) would be counted as having received 2 regimens; however, R-CHOP alternating with R-dexamethasone, high-dose cytarabine, and cisplatin (DHAP) as a planned induction regimen would count as one regimen
• Patient does not have any documented history of central nervous system (CNS) involvement by mantle cell lymphoma; this includes no evidence of parenchymal brain, spinal cord, or cerebrospinal fluid involvement; radiculopathy symptoms from nerve root compression by lymphoma do not constitute CNS involvement
• Patient must have archived formalin-fixed paraffin-embedded (FFPE) tumor tissue specimen from the original diagnostic biopsy available for submission to Adaptive Biotechnologies for ClonoSEQ ID molecular marker identification of unique clonal immunoglobulin deoxyribonucleic acid (DNA) sequence
• NOTE: Patients for whom the molecular marker is identified will have peripheral blood collected after completion of induction (patient?s disease status is PR or CR) and submitted to Adaptive Biotechnologies for minimal residual disease (MRD) assessment
• INCLUSION CRITERIA FOR TREATMENT ASSIGNMENT (STEP 1)
• Patients must have met eligibility criteria for the screening step
• Institution has received results from Adaptive Biotechnologies as defined by one of the following criteria:
• Patients are ?MRD Indeterminate?: ClonoSEQ ID molecular marker assessment did not identify any unique clonal immunoglobulin DNA sequence OR
• ClonoSEQ ID molecular marker assessment identified unique clonal immunoglobulin DNA sequence and MRD assessment is completed
• Patients must have completed induction therapy within 120 days prior to preregistration to step 0, AND no more than 300 days may have elapsed from the first dose of induction chemotherapy (cycle 1 [C1] day 1 [D1]) given, until the last day of induction chemotherapy administered; for those assigned to Arms A, C, or D, the date of transplant (?day 0?) must not be greater than 365 days after the first dose of induction chemotherapy (C1D1) given
• Patient must have received at least four (4) cycles of induction therapy
• Up to two regimens of chemotherapy are allowed as long as a continuous response was ongoing throughout therapy
• NOTE: For example, a patient who started treatment with rituximab/bendamustine and was then switched to R-CHOP (due to insufficient response or excessive toxicity) would be counted as having received 2 regimens; however, R-CHOP alternating with R-DHAP as a planned induction regimen would count as one regimen
• Patients must have achieved a radiologic complete or partial remission as defined by the Lugano criteria
• Patients must meet institutional eligibility requirements for stem cell transplant, including cardiac, renal, liver, and pulmonary requirements
• Patients have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2
• Human immunodeficiency virus (HIV) positive patients are not excluded, but to enroll, must meet all of the below criteria:
• HIV is sensitive to antiretroviral therapy
• Must be willing to take effective antiretroviral therapy if indicated
• CD4 count at screening >= 300 cells/mm^3
• No history of acquired immune deficiency syndrome (AIDS)-defining conditions
• Patient must be disease-free >= 3 years of prior malignancies with the exception of adequately treated non-melanoma skin cancer, adequately treated in situ carcinoma, low grade prostate carcinoma (Gleason grade =< 6) managed with observation that has been stable for at least 6 months
• Women must not be pregnant or breast-feeding
• All females of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy
• A female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months)
• Women of childbearing potential and sexually active males must be strongly advised to use an accepted and effective method of contraception or to abstain from sexual intercourse for the duration of their participation in the study

Inclusion Criteria:

• B-ALL blast cells expressing CD22
• Diagnosed with R/R B-ALL
• Prior therapy must include at least one standard chemotherapy regimen and at least one salvage regimen

Exclusion Criteria:

• Prior cellular therapy or investigational cellular or gene therapy within 60 days prior to enrollment

Inclusion Criteria:

• Biopsy proven B-NHL, including DLBCL, HGBL, or FL.
• For Arm B Only: Subject has biopsy proven DLBCL or HGBL
• For Arm C only: Subject has biopsy proven FL
• Subject has received at least 2 lines of therapy to which the subject has been either refractory or has subsequently relapsed. In order to be eligible for this study subjects must not be candidates for treatment regimens known to provide clinical benefit in B-NHL.
• Subject has an Eastern Cooperative Oncology Group (ECOG) Performance Status of ≤ 2.
• Subject must have adequate liver, bone marrow and kidney function (eGFR ≥ 50 mL/min).
• Subject must have locally confirmed CD19 positivity (must be documented after time of progression from last CD19-targeted therapy, if received)
• Subject must have at least 1 measurable disease site
• Subject must have ANC >/= 1000/mm3, platelets >/= 50,000 mm3, hemoglobin >/= 8.0 g/dL. Transfusion and/or growth factor are allowed but counts must be stable for at least 72 hours afterwards prior to screening
• Subject must have a total bilirubin <1.5x ULN, AST/ALT < 3xULN

Exclusion Criteria:

• Subject has been diagnosed with or treated for another malignancy whose natural history or treatment may interfere with the safety or efficacy assessment of the investigational regimen.
• Subject has a history of central nervous system (CNS) involvement by their B-NHL
• Subject has a history of leukemic presentation of their B-NHL.
• Subject has history or presence of clinically significant CNS pathology
• Subject has CNS involvement from active or history of autoimmune disease.
• Subject experienced Grade ≥ 3 cytokine release syndrome (CRS) following prior T-cell engager (TCE) or CAR T-cell therapy.
• Subject experienced Grade ≥ 2 neurotoxicity/immune effector cell-associated neurotoxicity syndrome (ICANS) following prior TCE or CAR T-cell therapy.
• Subject has received a peripheral autologous stem cell transplant (SCT) within 12 weeks, or an allogeneic SCT within 1 year of the first dose of study drug treatment or has received an SCT and requires ongoing immunosuppressive therapy.
• Subjects with human immunodeficiency virus (HIV) infection, or subjects with chronic or active infection with hepatitis B virus (HBV) or hepatitis C virus (HCV). HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. Subjects with chronic HBV may be enrolled if the HBV viral load is undetectable on suppressive therapy, or if the subject has a documented cure. Subjects with HCV who have a documented cure may be enrolled.
• Subject has a history of major cardiac abnormalities.
• If female, subject must not be pregnant or breastfeeding.

Inclusion Criteria:

• DOSE ESCALATION PHASE: Patients with relapsed or refractory non-Hodgkin lymphoma including both B-cell non-Hodgkin lymphoma (NHL) and T-cell NHL. Refractory cutaneous T-cell lymphoma (CTCL) will be allowed if greater or equal to stage 1B and have previously failed two systemic therapies
• DOSE EXPANSION PHASE: Patients with relapsed or refractory transformed lymphoma or germinal center B-cell diffuse large B-cell Lymphoma (GCB-DLBCL) as defined by Hans criteria. Equal numbers of patients will be enrolled onto one of 2 arms: (1) mutated EZH2 or (2) wild-type EZH2. EZH2 mutations will be identified by polymerase chain reaction (PCR)
• Patients must not be eligible for, or have refused, stem cell transplantation or chimeric antigen receptor T-cell (CAR T-cell) therapy
• Patients who have undergone 1-5 prior treatments of any type (progression after transplant/cellular therapy allowed) are eligible
• Patients must have measurable disease according to the Lugano classification
• Age >= 18 years. Because no dosing or adverse event data are currently available on the use of tazemetostat in combination with belinostat in patients < 18 years of age, children are excluded from this study
• Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%)
• Absolute neutrophil count (ANC) >= 1,000/mcL
• If there is documented lymphomatous involvement of the bone marrow as assessed by bone marrow biopsy within 90 days prior to registration, participants should have: ANC >= 0.75 × 10^9/L
• Platelets >= 75,000/mcL
• If there is documented lymphomatous involvement of the bone marrow as assessed by bone marrow biopsy within 90 days prior to registration, participants should have: platelets >= 50 x 10^9/L
• Total bilirubin =< .5 institutional upper limit of normal (ULN); unless due to Gilbert's disease, hemolysis, or lymphomatous involvement of liver in which case total bilirubin should be =< 5 x institutional ULN
• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 3 x institutional ULN; unless due to Gilbert's disease, hemolysis, or lymphomatous involvement of liver, in which case AST(SGOT)/ALT(SGPT) should be =< 5 x institutional ULN
• Glomerular filtration rate (GFR) >= 30 mL/min/1.73 m^2
• Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
• For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
• 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
• Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression
• 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. Patients whose lymphoma has transformed from a less aggressive histology remain eligible
• Patients should be New York Heart Association Functional Classification of class II or better
• Patients must have a QT interval corrected by Fridericia's formula (QTcF) =< 450 msec
• Able to swallow and retain orally-administered medication and does not have any clinically significant gastrointestinal abnormalities that may alter absorption, such as malabsorption syndrome or major resection of the stomach or bowels
• The effects of tazemetostat and belinostat on the developing human fetus are unknown. For this reason, women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation and for 6 months after the last dose of the study treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 3 months after completion of tazemetostat and belinostat administration
• Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity who have a legally-authorized representative (LAR) and/or family member available will also be eligible
• Patients that have received prior chemotherapy or radiotherapy must have completed their last treatment at least 2 weeks before entering the study. Rituximab given between EZH2 analysis and initiation of study drugs will be allowed

Exclusion Criteria:

• Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities > grade 1) with the exception of alopecia
• Patients who are receiving any other investigational agents
• Patients with central nervous system (CNS) metastases, including lymphomatous meningitis, as the study drugs are not known to effectively treat CNS disease
• History of allergic reactions attributed to belinostat or tazemetostat, or to compounds of similar chemical or biologic composition to these agents
• Patients receiving any medications or substances that are strong or moderate inhibitors or inducers of CYP3A4 within 14 days prior to study treatment are ineligible. Patients receiving strong UGT1A1 inhibitors are ineligible due to expected increased exposure to belinostat and potential for increased toxicity. Because the list of these agents is 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 known UGT1A1 genetic polymorphisms, such as UGT1A1*28, are excluded as they can have reduced UGTA1A activity and may be at risk for increased belinostat exposure
• Patients with uncontrolled intercurrent illness
• Pregnant women are excluded from this study because belinostat, as an HDAC inhibitor, and tazemetostat, as an EZH2 inhibitor, both have 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 belinostat and tazemetostat, breastfeeding should be discontinued if the mother is treated with belinostat and tazemetostat. Women of childbearing potential must have negative urine or serum pregnancy test to be eligible for this study
• Systemic steroids that have not been stabilized to the equivalent of =< 10 mg/day prednisone prior to the start of the study drugs
• Has thrombocytopenia, neutropenia, or anemia of grade >= 3 (per Common Terminology Criteria for Adverse Events [CTCAE] 5.0 criteria) or any prior history of myeloid malignancies, including myelodysplastic syndrome (MDS)
• Has abnormalities known to be associated with MDS (e.g. 5q deletion [del 5q], chromosome 7 abnormality [chr 7 abn]) and multiple primary neoplasms (MPN) (e.g. JAK2 V617F) observed in cytogenetic testing and deoxyribonucleic acid (DNA) sequencing
• Has a prior history of T lymphoblastic lymphoma/T acute lymphoblastic leukemia (T-LBL/T-ALL)