Inclusion Criteria:

• Participants who have received at least one dose of cilta-cel in a Company-sponsored clinical study
• Participants who have provided informed consent for this study

Inclusion Criteria:

• For Part A and B: Have relapsed/refractory NHL and >=2 prior systemic therapies, (including rituximab), and be ineligible for known therapies with demonstrated clinical benefit per investigator assessment or, histologically confirmed AITL that has recurred or progressed following institutional standard of care therapy.
• For Part C and D: Have R/R DLBCL, not otherwise specified [NOS (DLBCL, NOS)] or large B-cell lymphoma (LBCL) arising from follicular lymphoma and have received two or more lines of systemic therapy.
• Have at least one bi dimensionally measurable lesion >1.5-centimeter (cm) in largest dimension for nodal or >1.0 cm for extranodal lesion.
• Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 or 1 (NOTE: For Part A only - ECOG PS of 2 is allowed for participants with secondary CNS lymphoma).
• Adequate bone marrow function
• Adequate kidney function
• Adequate Liver Function

Exclusion Criteria:

• Current or past history of peripheral eosinophilia, hypereosinophilic syndrome (HES), organ-specific eosinophilic disorder, or drug reaction with eosinophilia and systemic symptoms (DRESS).
• Prior allogeneic stem cell transplant (SCT) or solid organ transplantation.
• Any other active malignancy within 3 years prior to enrollment, except for adequately treated basal cell or squamous cell skin cancer, melanoma in situ or carcinoma in situ of the breast or cervix, and prostate cancer with active surveillance.
• Any of the following in the previous 6 months:
• Myocardial infarction, long QT syndrome or family history of long QT syndrome, or Torsade de Pointes;
• Clinically important atrial or ventricular arrhythmias;
• Serious conduction system abnormalities, 3rd degree atrioventricular (AV block), unstable angina, coronary/peripheral artery bypass graft, symptomatic congestive heart failure (CHF), New York Heart Association Class III or IV;
• Cerebrovascular accident, transient ischemic attack, symptomatic pulmonary embolism, and/or other clinically significant episode of thromboembolic disease;
• Active inflammatory gastrointestinal (GI) disease, chronic diarrhea, previous gastric resection, or lap band surgery.
• Uncontrolled hypertension despite optimal medical treatment
• History of myocarditis.
• In ability to comply with listed prohibited treatments.
• Standard 12-lead electrocardiogram (ECG) that demonstrates clinically relevant abnormalities that may affect participant safety or interpretation of study results.
• Cardiac ejection fraction <45%.

Inclusion Criteria:

• Adult 18 years of age and older.
• Histologically confirmed diagnosis of B-NHL before enrollment.
• Must have received prior CAR T or were unwilling/unable to receive prior CAR T.
• Must have refractory or relapsed disease after receiving 2 prior lines of therapies.
• If relapsed/refractory post-auto-SCT, then must have undergone auto-SCT at least 6 months prior to enrollment.
• If relapsed/refractory disease after allogeneic stem cell transplant (allo SCT) then must have undergone allo-SCT at least 6 months prior to enrollment and without evidence of graft versus host disease.
• Measurable disease at time of enrollment: At least one measurable lesion per Lugano Response Criteria (Cheson et al., 2014).
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1

Exclusion Criteria:

• Previously treated with any investigational agent within 30 days prior to screening.
• Adequately treated non-melanoma skin cancer such as basal cell or squamous cell carcinoma
• Carcinoma-in-situ (e.g., cervix, bladder, breast) treated curatively and without evidence of recurrence for at least 3 years prior to enrollment.
• Any other malignancy which has been completely treated and remains in complete remission for ≥ 5 years prior to enrollment. Completely treated prostate cancer with prostate-specific antigen (PSA) level < 1.0 may also be permitted.
• Known immunodeficiency disease.
• History or presence of active or clinically relevant primary central nervous system (CNS) disorder, such as seizure, encephalopathy, cerebrovascular ischemia/hemorrhage, cerebellar disease, or any autoimmune disease with CNS involvement. For primary CNS disorders that have recovered or are in remission, participants without recurrence within 2 years of planned study enrollment may be included.
• Uncontrolled hypertension, history of myocarditis or congestive heart failure, unstable angina, serious uncontrolled cardiac arrhythmia, or myocardial infarction within 6 months prior to study entry.
• Any active uncontrolled systemic fungal, bacterial or viral infection.Note: Other protocol defined Inclusion/Exclusion criteria may apply.

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, as described in the protocol. 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. Availability of tumor tissue for submission to central laboratory is required for study enrollment. Archival tumor tissue for histological assessment prior to enrollment is allowed 6. 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, as described in the protocol 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, as described in the protocol 5. Standard radiotherapy within 14 days of first administration of study drug, as described in the protocol 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 rasburicaseNOTE: Other protocol defined inclusion / exclusion criteria apply

Inclusion Criteria:

• Eastern Cooperative Oncology Group (ECOG) performance of 0 or 1.
• Must have confirmed diagnosis of Relapsed/Refractory Multiple Myeloma (RRMM) after the participant's last treatment, as outlined in the protocol.
• All participants must have measurable diseases per central laboratory as outlined in protocol

Exclusion Criteria:

• Has received prior etentamig treatment.
• Prior exposure to BCMA-targeted therapy as noted in the protocol.
• Has received prior cereblon E3 ligase modulatory drug (CELMoD) (iberdomide or mezigdomide).

Inclusion Criteria:

For patients in Phase I: 1. Have a diagnosis of relapsed or refractory AML, ALL or acute leukemia of ambiguous lineage according to World Health Organization (WHO) 2022 classification, or, in selected sites and regions, a diagnosis of MDS or MM as determined by pathology review at the treating institution, and whose disease has progressed after available standard therapies known to be active for their AML, ALL, or acute leukemia of ambiguous lineage or, in selected sites and regions, for MM or MDS. If acute leukemia patients are transformation from MDS or other hematologic malignancies, patients need to receive available standard therapies as acute leukemia after AML transformation and before enrolling this trial. In regions or countries where required by regulatory authorities, participants must have a documented KMT2A (MLL) fusion or NPM1 mutation, including those with coexisting FLT3 genomic alterations and/or IDH1/2 mutation. Participants who are candidates for stem cell transplantation must have been offered this therapeutic option. For patients with MDS (selected sites and regions): 1. Patients with MDS must have bone marrow blasts ≥ 5% 2. Patients with MDS must have relapsed or refractory disease and have exhausted available standard therapies including at least 2 cycles of treatment with HMA For patients with MM (selected sites and regions): 3. Have a confirmed diagnosis of multiple myeloma according to International Myeloma Working Group (IMWG) 2016 classification (Kumar, 2016) and whose disease has progressed after treatment with a minimum of 3 prior anti-myeloma regimens including a proteasome inhibitor (PI), an immunomodulatory drug (IMiD), and an anti-CD38 monoclonal antibody (mAb); patients must not be candidates for available therapies with established clinical benefit 4. Have measurable disease as defined in the protocol 5. Meet the laboratory parameters set in the protocol For patients with relapsed/refractory AML in the venetoclax and azacitidine combination cohort (in countries and sites where permitted): 6. Have MLLr or NPM1m. For patients with relapsed/refractory AML in the gilteritinib combination cohort (in countries and sites where permitted): 7. Have MLLr or NPM1m AND any of the following FLT3 mutations: FLT3-ITD, FLT3-TKD/D835 or FLT3-TKD/I836. For patients with relapsed/refractory AML with NPM1 enrolled in the RP2D confirmation cohort: 8. Must have ≥5% blasts in bone marrow by morphologic assessment 9. Must not have received prior treatment with a menin inhibitor For patients with newly diagnosed AML: 10. Must have AML as defined by WHO 2022 criteria with a documented MLLr or NPM1m (patients with AML characterized by MLL partial tandem duplications, MLL deletions, or trisomy 11 are not eligible) 11. Must not have received treatment for AML with the exception of hydroxyurea for control of white blood cell counts. For patients in Phase 2: 2. Have a confirmed diagnosis of relapsed AML or ALL according to WHO 2022 classification, as determined by pathology review at the treating institution, and who have ≥5% blasts by morphologic assessment in the bone marrow. Patients with extramedullary disease or peripheral blasts as the only manifestation of relapse are not eligible. Patients must have received clinically applicable standard therapies with confirmed survival benefit. Patients must not have had prior exposure to a menin inhibitor. 3. Have a documented KMT2A (MLL)-fusion assessed at relapse or immediately prior to the determination of refractory status. KMT2A genetic alterations other than fusions (eg, KMT2A-PTD, amplification, point mutation) are not permitted. For all patients: 4. Be > 18 years of age. For countries and sites where approved, for DSP-5336 monotherapy, acute leukemia patients ≥12 years of age who weigh ≥40 kg may be enrolled. 5. Have an Eastern Cooperative Oncology Group (ECOG) performance status ≤2. 6. For monotherapy, WBC below 30,000/μ at enrollment. For the combination arms, WBC count must be below 25,000/uL at enrollment and prior to starting treatment. (Hydroxyurea and steroids for cytoreduction purposes are allowed prior to enrollment and during study treatment) 7. Clearance of creatinine level ≥ 50 ml/min, assessed by the CPK-EPI formula (2021 version and Cystatin C not required) 8. Total bilirubin ≤1.5 the upper limit of normal (ULN) (or ≤2.0 ULN for patients with known Gilbert's syndrome) 9. Aspartate aminotransferase (AST) ≤3.0 times ULN 10. Alanine aminotransferase (ALT) ≤3.0 times ULN 11. Any prior treatment-related toxicities resolved to Grade ≤1 prior to enrollment, with the exception of Grade ≤2 alopecia or neuropathy 12. Be willing to attend study visits as required by the protocol 13. Have an estimated life expectancy ≥3 months, based on the investigator's assessment 14. Females of childbearing potential must have a negative serum pregnancy test. Females of childbearing potential are defined as women who have (1) experienced menarche and have not undergone sterilization procedures (hysterectomy, or bilateral oophorectomy), or have (2) not experienced menopause as defined in the protocol. 15. All men and all women of childbearing potential and male patients' partners who are women of childbearing potential are required to use a highly effective method of contraception during the study and for 6 months (for females and males alike) after the last dose of study drug. Further guidelines noted in protocol. 16. Have AML/ALL/MDS/MM bone marrow material suitable for genomic analysis of AML,ALL, MDS, or MM genetic alterations. Note: If a bone marrow material is insufficient, an alternative suitable tissue (ex: peripheral blood) must be provided.

Exclusion Criteria:

1. Has a left ventricular ejection fraction (LVEF) <50%, as determined by ECHO 2. Histological diagnosis of acute promyelocytic leukemia 3. Received systemic calcineurin inhibitors within 2 weeks prior to the first dose of DSP 5336 4. Have abnormal ECGs at screening that are clinically significant, such as (QTc >480 msec, with QTc corrected according to Fridericia's formula (QTcF). For clinical sites in the UK, have abnormal ECGs at screening that are clinically significant, such as QTc ≥470 msec and ≥450 msec with QTc corrected according to Fridericia's formula (QTcF), for females and males, respectively. In addition, patients with a history of prolonged QT syndrome or who are required to take therapies associated with QT-interval prolongation are excluded. Note: In case of bundle branch block, QT interval correction can be performed. 5. Has an active and uncontrolled, bacterial, viral, or fungal infection requiring parenteral therapy. Note: Patients must be afebrile with negative blood cultures at least 72 hours prior to Cycle 1 Day 1. 6. Receives concurrent sensitive substrates with a narrow safety window or strong inhibitors or inducers of CYP3A4/5, including specifically: ketoconazole, isavuconazole and itraconazole. Other antifungals that are used as standard of care to prevent or treat infections are permitted. If a patient is on one of the excluded azole class antifungals, he/she can be taken off or switched to a permitted azole 7 or more days prior to first dose, then the patient could be allowed on study (Arm B) with approval of the medical monitor. 7. Had major surgery within 28 days prior to the first dose of DSP-5336 8. Has active central nervous system leukemia (prophylactic intrathecal chemotherapy is allowed). 9. Underwent HSCT or chimeric antigen receptor cell (CAR-T) therapy or other modified T-cell therapy within 60 days prior to the first dose of DSP-5336. For clinical sites in the UK, underwent CAR-T therapy or other modified T-cell therapy within 6 months prior to the first dose of DSP-5336. 10. Received a donor lymphocyte infusion within 28 days prior to the first dose of DSP-5336, or receiving immunosuppressive therapy post-HSCT at the time of screening, or with clinically active GVHD or GVHD requiring active medical intervention other than the use of topical steroids for ongoing cutaneous GVHD 11. Received antineoplastic agents (except hormonal therapies as adjuvant maintenance for breast or prostate cancers if a patient is taking before starting study treatment, and hydroxyurea given for controlling blast cells) or other investigational treatment within 7 days or 5 half-lives, whichever is shortest, prior to the first dose of DSP-5336 12. In the opinion of the treating investigator, have any concurrent conditions that could pose an undue medical hazard or interfere with interpretation of study results; these conditions include, but are not limited to: clinically significant non-healing or healing wounds; concurrent congestive heart failure (New York Heart Association Functional Classification Class III or IV; see Section 21.2); concurrent unstable angina; concurrent cardiac arrhythmia requiring treatment (excluding asymptomatic atrial fibrillation); recent (within the prior 6 months) myocardial infarction; acute coronary syndrome within the previous 6 months; significant pulmonary disease (shortness of breath at rest or on mild exertion), eg, due to concurrent severe obstructive pulmonary disease, concurrent hypertension not controlled with concomitant medication, or diabetes mellitus with more than 2 episodes of ketoacidosis in the prior 6 months 13. Have a known detectable viral load for human immunodeficiency virus or hepatitis C, or evidence of hepatitis B surface antigen, all being indicative of active infection. For sites in Japan, Taiwan, and Korea only: Hepatitis B core (HBc) antibody or hepatitis B surface (HBs) antibody test should be performed if HBsAg is negative. If HBc antibody or HBs antibody test is positive, HBV DNA quantification test should be performed to confirm that HBV DNA is negative. 14. Have severe dysphagia, short-gut syndrome, gastroparesis, or other conditions that limit the ingestion or gastrointestinal absorption of drugs administered orally, including the inability to swallow oral medication 15. Have cognitive, psychological, or psychosocial impediment that would impair the ability of the patient to receive therapy according to the protocol, or adversely affect the ability of the patient to comply with the informed consent process, protocol, or protocol-required visits and procedures 16. Are pregnant or breastfeeding or planning to become pregnant. Note: Patients who are breastfeeding may be enrolled if they interrupt breastfeeding prior to the first dose of any study drugs and do not feed the baby with breast milk expressed after receiving the first dose of any study drugs. Breastfeeding should not be resumed for at least 6 months after the last dose of study drug 17. Have any history or complication of interstitial lung disease (for sites in Japan in Phase 1 dose escalation). For clinical sites in the EU, have a history of Grade ≥ 2 drug-induced interstitial lung disease or Grade ≥ 2 non-infectious pneumonitis within 6 months of starting study treatment. 18. Have a history of Torsades de Pointes 19. Received systemic calcineurin inhibitors within 4 weeks prior to the first dose of DSP-5336 20. Have plasma cell leukemia (>2.0 x 109 /L plasma cells in blood by standard differential) (for patients with MM) 21. For patients intending to enroll into the combination cohort with gilteritinib: Patients must be gilteritinib-naïve or sensitive and have not received a FLT3 inhibitor in the relapsed refractory setting (prior FLT3 inhibitor in front line therapy is allowed) 22. Have a known intolerance of hypersensitivity reaction to components of the investigational medicinal product 23. For clinical sites in the UK: In Arm E (DSP-5336 + venetoclax/azacitidine), have received a live vaccine within 30 days prior to the first dose of DSP-5336

Inclusion Criteria:

• Participant must be greater than or equal to (>=) 18 years of age, at the time of signing informed consent
• Tumor must be histologically confirmed cluster of differentiation (CD)19 and/or CD20 positive
• Must meet the indications for each subtype in Phase 1b as specified in protocol and Phase 2 participants must have following: Diagnosis of Large B-cell lymphoma (LBCL), Follicular large B-cell lymphoma (FLBCL), or transformation of indolent lymphoma; Received at least 2 prior lines of systemic therapy; Relapsed or refractory disease defined as 1 or more of the following: Stable disease or Progressive disease (PD) as best response to most recent anti-lymphoma therapy OR disease progression or recurrence after a partial response (PR) or complete response (CR) to most recent anti lymphoma therapy; cohort specific requirements as mentioned in protocol
• Measurable disease as defined by Lugano 2014 classification
• Eastern cooperative oncology group (ECOG) performance status of 0 to 2

Exclusion Criteria:

• History of symptomatic deep vein thrombosis or pulmonary embolism within six months of apheresis (line associated deep vein thrombosis is allowed)
• 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 apheresis
• History of a seizure disorder, 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)
• Evidence of active viral or bacterial infection requiring systemic antimicrobial therapy, or uncontrolled systemic fungal infection
• Diagnosis of Human herpes virus (HHV) 8-positive DLBCL or T cell/histiocyte-rich large B-cell lymphoma or Burkitt and high-grade B-cell lymphoma with 11q aberrations (previously Burkitt-like lymphoma) or Richter's transformation or Lymphomatoid granulomatosis or Plasmablastic lymphoma or Waldenstrom's Macroglobulinemia
• Any prior solid organ or allogeneic stem cell transplantation
• Autologous stem cell transplant within 12 weeks of apheresis; Prior CAR-T cell therapy within 12 weeks of apheresis

Inclusion Criteria:

• All patients must be enrolled on APEC14B1 and consented to eligibility screening (part A) prior to treatment and enrollment on AALL2321
• Infants (aged 365 days or less) on the date of diagnosis are eligible; infants must be > 36 weeks gestational age at the time of enrollment
• Patients must have newly diagnosed B-acute lymphoblastic leukemia (B-ALL, 2017 World Health Organization [WHO] classification), also termed B-precursor ALL, or acute leukemia of ambiguous lineage (ALAL), which includes mixed phenotype acute leukemia. For patients with ALAL, the immunophenotype of the leukemia must comprise at least 50% B lineage
• Diagnostic immunophenotype: Leukemia cells must express CD19

Exclusion Criteria:

• Patients with Down Syndrome
• Patients with secondary B-ALL that developed after treatment of a prior malignancy with cytotoxic chemotherapy
• Patients must not have received any cytotoxic chemotherapy for either the current diagnosis of infant ALL or for any cancer diagnosis prior to the initiation of protocol therapy, with the exception of:
• Steroid pretreatment:
• PredniSONE, prednisoLONE, or methylPREDNISolone for ≤ 72 hours (3 days) in the 7 days prior to enrollment. The dose of predniSONE, prednisoLONE or methylPREDNISolone does not affect eligibility
• Inhaled and topical steroids are not considered pretreatment
• Note: Pretreatment with dexamethasone in the 28 days prior to initiation of protocol therapy is not allowed with the exception of a single dose of dexamethasone used during or within 6 hours prior to or after sedation to prevent or treat airway edema. However, prior exposure to ANY steroids that occurred > 28 days before enrollment does not affect eligibility
• Intrathecal cytarabine or methotrexate:
• An intrathecal dose of cytarabine or methotrexate in the 7 days prior to enrollment does not affect eligibility
• Note: The preference is to defer the diagnostic lumbar puncture with intrathecal chemotherapy to day 1 of induction to allow for cytoreduction of circulating blasts and decrease the potential for central nervous system (CNS) contamination due to a traumatic tap. If done prior to day 1 of induction, these results will be used to determine CNS status
• Hydroxyurea:
• Pretreatment with ≤ 72 hours (3 days) of hydroxyurea in the 7 days prior to enrollment does not affect eligibility
• All patients and/or their parents or legal guardians must sign a written informed consent
• All institutional, Food and Drug Administration (FDA) and National Cancer Institute (NCI) requirements for human studies must be met

Inclusion Criteria:

• Patients must be >= 1 year and < 22 years of age at the time of enrollment
• Patients must have B-ALL, or previously diagnosed B lymphoblastic lymphoma (B-LL), with >= 5% (M2 or M3) bone marrow blasts with or without extramedullary disease
• NOTE: Relapsed patients previously diagnosed with B-lymphoblastic lymphoma (B-LL) are eligible if they have an M2 or M3 marrow at the time of enrollment on this study
• Patients with ALL or B-LL who have M2 morphology must have local confirmatory testing showing >= 5% blasts by flow cytometry, fluorescence in situ hybridization (FISH) testing or other molecular method
• Leukemic blasts must demonstrate surface expression of CD22 at the time of relapse by local/institutional flow cytometry of a bone marrow aspirate sample; (assessment of CD22 using a bright fluorophore such as phycoerythrin [PE] is strongly recommended)
• In the case of an inadequate aspirate sample (dry tap) or if bone marrow aspirate is unable to be performed due to patient clinical status, flow cytometry of peripheral blood specimen may be substituted if the patient has at least 1,000/uL circulating blasts; alternatively, CD22 expression may be documented by immunohistochemistry of a bone marrow biopsy specimen
• Patients with one of the following:
• Second or greater relapse;
• Primary refractory disease with at least 2 prior induction attempts;
• First relapse refractory to at least one prior re-induction attempt
• Any relapse after HSCT (Cohort 1 ONLY)Patients with Down syndrome are eligible ONLY for Cohort 1 with:
• Any of above disease status, OR
• First relapse with no prior re-induction attempt NOTE: Patients with Down syndrome or prior HSCT are NOT eligible for Cohort 2 combination therapy
• Patients with Philadelphia chromosome (Ph)+ ALL must have had two prior therapy attempts including two different tyrosine kinase inhibitors (TKIs)
• Patients must have fully recovered from the acute toxic effects of all prior anti-cancer therapy, defined as resolution of all such toxicities to =< grade 2 or lower per the inclusion/exclusion criteria prior to entering this study. Apply to Cohort 2:
• Cytotoxic chemotherapy or other anti-cancer agents known to be myelosuppressive. For agents not listed, the duration of this interval must be discussed with the study chair and the study-assigned Research Coordinator prior to enrollment.
• A waiting period prior to enrollment is not required for patients receiving standard cytotoxic maintenance chemotherapy (i.e., corticosteroid, vincristine, 6MP, and/or methotrexate).
• A waiting period is not required for patients receiving a single dose of intrathecal methotrexate, hydrocortisone, and/or cytarabine within 7 days prior to enrollment
• >= 14 days must have elapsed after the completion of other cytotoxic therapy, with the exception of hydroxyurea, for patients not receiving standard maintenance therapy. For patients who previously received calaspargase pegol, >= 21 days must have elapsed after the last dose. Additionally, patients must have fully recovered from all acute toxic effects of prior therapy.
• Note: Cytoreduction with hydroxyurea must be discontinued >= 24 hours prior to the start of protocol therapy.
• Anti-cancer agents not known to be myelosuppressive (e.g., not associated with reduced platelet or absolute neutrophil count [ANC] counts): >= 7 days after the last dose of agent. For agents not listed, the duration of this interval must be discussed with the study chair and the study-assigned research coordinator prior to enrollment.
• Anti-cancer agents that are antibodies: >= 21 days must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to grade =< 1. There is an exception for blinatumomab infusions, for which patients must have been off for at least 3 days and all drug related toxicity must have resolved to grade 2 or lower as outlined in the inclusion/exclusion criteria.
• Corticosteroids: If used to modify immune adverse events related to prior therapy, >= 14 days must have elapsed since last dose of corticosteroid. A waiting period prior to enrollment is not required for patients receiving corticosteroid for leukemia therapy/cytoreduction.
• Radiotherapy: >= 2 weeks must have elapsed since local palliative radiation therapy (XRT) (small port); >= 3 months must have elapsed if prior cranial or craniospinal XRT was received, if >= 50% of the pelvis was irradiated, or if total body irradiation (TBI) was received; >= 6 weeks must have elapsed if other substantial bone marrow irradiation was given.
• Stem cell transplant or rescue without TBI: For Cohort 1, at least 90 days must have elapsed since stem cell transplant and at least 30 days from donor lymphocyte infusion. Patient must have had no more than one previous HSCT and currently have no evidence of active graft vs. host disease (GVHD). For Cohort 2, no prior HSCT is allowed.
• Chimeric antigen receptor (CAR) T cell therapy: At least 30 days must have elapsed from the last CAR-T cell infusion
• Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1, or 2; use Karnofsky for patients > 16 years of age and Lansky for patients =< 16 years of age; patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score
• Creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70 mL/min/1.73 m^2 or
• A serum creatinine based on age/gender as follows:
• 1 to < 2 years: maximum serum creatinine 0.6 mg/dL (both male and female)
• 2 to < 6 years: maximum serum creatinine 0.8 mg/dL (both male and female)
• 6 to < 10 years: maximum serum creatinine 1 mg/dL (both male and female)
• 10 to < 13 years: maximum serum creatinine 1.2 mg/dL (both male and female)
• 13 to < 16 years: maximum serum creatinine 1.5 mg/dL (male), 1.4 mg/dL (female)
• >= 16 years: maximum serum creatinine 1.7 mg/dL (male), 1.4 mg/dL (female)
• Direct bilirubin =< 1.5 x upper limit of normal (ULN) for age, and
• Serum glutamic pyruvic transaminase (SGPT) (alanine aminotransferase [ALT]) =< 5 x ULN for age; for the purpose of this study, the ULN for ALT will be 45 U/L

Exclusion Criteria:

• Patients with any prior history of SOS irrespective of severity
• Patients with isolated central nervous system (CNS), testicular, or any other extramedullary site of relapse
• Patients who have been previously treated with inotuzumab ozogamicin
• Patients who have previously received HSCT (Cohort 2 only)
• Patients with Down syndrome (Cohort 2 only)
• History of allergic reaction attributed to compounds of similar or biologic composition to inotuzumab ozogamicin or other agents in the study
• Note: Patients with history of allergy to pegaspargase/calaspargase pegol are eligible for enrollment on Cohort 2 if Erwinia formulation of asparaginase can be obtained
• Patients with active optic nerve and/or retinal involvement are not eligible; patients who are presenting with visual disturbances should have an ophthalmologic exam and, if indicated, a magnetic resonance imaging (MRI) to assess optic nerve or retinal involvement
• Patients who are currently receiving another investigational drug
• Patients who are currently receiving or plan to receive other anti-cancer agents (except hydroxyurea, which may be continued until 24 hours prior to start of protocol therapy, and intrathecal chemotherapy)
• Anti-GVHD or agents to prevent organ rejection post-transplant; patients who are receiving cyclosporine, tacrolimus, or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post-transplant are not eligible for this trial; at least 3 half-lives must have elapsed after the last dose of GVHD or anti-rejection medications
• Patients who are currently receiving or plan to receive corticosteroids except as described below
• Systemic corticosteroids may be administered for cytoreduction up to 24 hours prior to the start of protocol therapy, (Cohort 1 only) for all patients, corticosteroids may be administered as a premedication for inotuzumab ozogamicin and as treatment for allergic reactions or for physiologic replacement/stress dosing of hydrocortisone for documented adrenal insufficiency; corticosteroids are not allowed for other indications
• Patients with known human immunodeficiency virus (HIV), hepatitis B or C infections; testing to prove negative status is not required for enrollment unless it is deemed necessary for usual medical care of the patient
• Patients who have an active uncontrolled infection defined as:
• Positive bacterial blood culture within 48 hours of study enrollment;
• Fever above 38.2 degree Celsius (C) within 48 hours of study enrollment with clinical signs of infection; fever that is determined to be due to tumor burden is allowed if patients have documented negative blood cultures for at least 48 hours prior to enrollment and no concurrent signs or symptoms of active infection or hemodynamic instability
• A positive fungal culture within 30 days of study enrollment or active therapy for presumed invasive fungal infection
• Patients may be receiving IV or oral antibiotics to complete a course of therapy for a prior documented infection as long as cultures have been negative for at least 48 hours and signs or symptoms of active infection have resolved; for patients with clostridium (C.) difficile diarrhea, at least 72 hours of antibacterial therapy must have elapsed and stools must have normalized to baseline
• Active viral or protozoal infection requiring IV treatment
• Patients known to have one of the following concomitant genetic syndromes: Bloom syndrome, ataxia-telangiectasia, Fanconi anemia, Kostmann syndrome, Schwachman (Schwachman-Diamond-Blackfan) syndrome or any other known bone marrow failure syndrome
• There have been no human studies of inotuzumab ozogamicin in pregnant women and no reports of exposure in utero; based on nonclinical safety studies, inotuzumab ozogamicin has the potential to impair human male and female fertility and to adversely affect human embryo fetal development; women of childbearing potential should be advised to avoid becoming pregnant while receiving inotuzumab ozogamicin; there is no information regarding the presence of inotuzumab ozogamicin in human milk, the effects on the breast-fed infant, or the effects on milk production; because of the potential for adverse reactions in breast-fed infants, women should not breast-feed during treatment with inotuzumab ozogamicin and for at least 2 months after the final dose
• Female patients of childbearing potential are not eligible unless a negative pregnancy test result has been obtained within 7 days prior to enrollment
• Female patients who are sexually active and of reproductive potential are not eligible unless they agree to use an effective contraceptive method for the duration of their study participation and for 8 months after the last dose of inotuzumab ozogamicin
• Men with female partners of childbearing potential should use effective contraception during treatment with inotuzumab ozogamicin and for at least 5 months after the last dose of inotuzumab ozogamicin
• Lactating females are not eligible unless they agree not to breastfeed their infants

Inclusion:

• Documented diagnosis of multiple myeloma (MM) as defined by the criteria below: 1. MM diagnosis according to the international myeloma working group (IMWG) diagnostic criteria 2. Measurable disease at screening as assessed by central laboratory
• Received at least 3 prior lines of antimyeloma therapy including a proteasome inhibitor (PI), an immunomodulatory drug (IMiD), and an anti-cluster of differentiation (CD) 38 monoclonal antibody (mAb)
• Documented evidence of progressive disease(PD) or failure to achieve a response to the last line of therapy based on investigator's determination of response by the IMWG criteria
• Have discontinued concurrent use of any other anticancer treatment (including nonpalliative radiotherapy) or investigational agent
• Have an eastern cooperative oncology group (ECOG) performance status (PS) of 0 to 2 at screening and immediately before the start of study treatment administrationExclusion:
• Suspected or known allergies, hypersensitivity, or intolerance to excipients of JNJ-79635322
• Had major surgery within 2 weeks before first dose or has planned major surgery during study treatment phase
• Known active or prior central nervous system (CNS) involvement or exhibits clinical signs of meningeal involvement of MM
• Participant has leptomeningeal disease
• Participant has a prior or concurrent second malignancy the natural history or treatment of which could likely interfere with any study endpoints of safety or the efficacy of the study treatment

Inclusion Criteria

• Documented diagnosis of multiple myeloma (MM) as per International Myeloma Working Group (IMWG) criteria.
• Received at least 4 classes of MM treatment [including immunomodulatory drug (IMiD), proteasome inhibitor (PI), anti CD38 mAb, anti-BCMA therapy, and at least 3 prior lines of therapy (LOT).
• Documented disease progression during or after their last anti-myeloma regimen as per IMWG 2016 criteria.
• Participants must have measurable disease during screening.
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.

Exclusion Criteria

• Active or history of central nervous system involvement with MM.
• Active systemic fungal, bacterial, viral, or other infection despite appropriate anti-infective treatment at the time of leukapheresis. Participants with severe infection, severe sepsis or bacteremia in the last 28 days prior to leukapheresis are excluded.
• Received any prior therapy directed at G protein-coupled receptor class C, group 5, member D (GPRC5D) or has received other prior treatment for MM without the required washout prior to leukapheresis.
• Other protocol-defined Inclusion/Exclusion criteria apply.

Key Inclusion Criteria:

1. Previously untreated participants for lymphoma with documented Cluster of Differentiation 20+ (CD20+) DLBCL, as described in the protocol OR relapsed or refractory DLBCL, for whom next available standard of care therapy is not available or deemed ineligible according to the investigator (Part 1A only) 2. Measurable disease with at least one nodal lesion or at least one extranodal lesion, as described in the protocol 3. Eastern Cooperative Oncology Group (ECOG) performance status ≤2 4. Life expectancy ≥ 12 months 5. International Prognostic Index (IPI) of 3 to 5 (part 1 only) and ≥2 (part 2) for untreated DLBCL only 6. Adequate hematologic and organ function, as defined in the protocol.

Key Exclusion Criteria:

1. Primary Central Nervous System (CNS) lymphoma or known involvement by non-primary CNS NHL and history or current relevant CNS pathology 2. Another active malignancy, significant active disease or medical condition, as described in the protocol 3. Peripheral neuropathy Grade ≥3 4. Treatment with any systemic anti-lymphoma therapy, except for participants with Relapsed/Refractory (R/R) DLBCL and participants with DLBCL transformed from an indolent lymphoma after treatment with systemic anti-lymphoma therapy. 5. Any other therapy or investigational treatment within 28 days or 5 half-lives of the drug, whichever is shorter, prior to the start of study treatment 6. Recent major surgery, prior organ transplantation, or standard radiotherapy, as described in the protocol 7. Allergy/hypersensitivity to study drugs, as described in the protocol 8. Infections such as any active infection (bacterial, viral, fungal, mycobacterial, parasitic or other), active Coronavirus Disease (COVID-19) infection, uncontrolled infection with Human Immunodeficiency Virus (HIV), Hepatitis B Virus (HBV), or Hepatitis C Virus (HCV), Cytomegalovirus (CMV) infection, as described in the protocol.Note: Other protocol-defined Inclusion/ Exclusion criteria apply