Epcoritamab, Rituximab, Gemcitabine and Oxaliplatin (R-GemOx) as Salvage Therapy Before Autologous Stem Cell Transplant for the Treatment of Relapsed/Refractory Diffuse Large B-Cell Lymphoma

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative. * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Age: ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Histologically confirmed diagnosis of DLBCL, not-otherwise specified (NOS), transformation of indolent B-cell lymphoma, High grade B-cell lymphoma (HGBCL), NOS, primary mediastinal large B-cell lymphoma (PMBCL) * Biopsy-proven relapsed or refractory disease after 1 prior line of chemoimmunotherapy and: * CAR-naïve patients (Cohort 1) * If primary refractory, or relapsed within 12 months and are ineligible for or are unwilling to undergo CD19-directed CAR-T cell therapy * If relapsed beyond 12 months * CAR-experienced patients (Cohort 2) * If relapsed or refractory to CD19-directed CAR T cell therapy * Measurable disease on computed tomography (CT) scan, defined as a nodal site greater than 1.5 cm in the longest axis or an extranodal site greater than 1.0 cm in the longest axis AND baseline fluorodeoxyglucose-positron emission tomography (FDG-PET) must demonstrate positive lesion compatible with CT defined anatomical tumor sites * Considered eligible for high-dose chemotherapy followed by ASCT * Fully recovered from the acute toxic effects (except alopecia) to ≤ grade 1 to prior anti-cancer therapy * Positive for CD20 by immunohistochemistry * Without bone marrow involvement: Absolute neutrophil count (ANC) ≥ 1,000/mm\^3 * NOTE: Growth factor is not permitted within 14 days of ANC assessment unless cytopenia is secondary to disease involvement * Without bone marrow involvement: Platelets ≥ 100,000/mm\^3. With bone marrow involvement: Platelets ≥ 75,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 14 days of platelet assessment unless cytopenia is secondary to disease involvement * Hemoglobin ≥ 8g/dL * NOTE: Red blood cell transfusions are not permitted within 14 days of hemoglobin assessment unless cytopenia is secondary to disease involvement * Total bilirubin ≤ 1.5 X upper limit of normal (ULN) * If hepatic involvement by lymphoma, or Gilbert's disease: ≤ 3 X ULN * Aspartate aminotransferase (AST) ≤ 3.0 x ULN * Alanine aminotransferase (AST) ≤ 3.0 x ULN * Creatinine clearance of ≥ 45 mL/min per 24 hour urine test or the Cockcroft-Gault formula * If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin (PT) ≤ 1.5 x ULN. If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants * If not receiving anticoagulants: Activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN. If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants * Seronegative for HIV antigen/antibody (Ag/Ab) combo, hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative) OR * If seropositive for HIV, HCV or HBV, nucleic acid quantitation must be performed. Viral load must be undetectable. HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial * Meets other institutional and federal requirements for infectious disease titer requirements * Note Infectious disease testing to be performed within 28 days prior to day 1 of study therapy * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential\* to use an effective method of birth control or abstain from heterosexual intercourse for the course of the study and after completion of study treatment as described below separately for males and females. * Female participants must remain abstinent or use contraceptive methods with a failure rate of \< 1% per year during the treatment period and for at least 6 months after the last dose of gemcitabine, 9 months after the last dose of oxaliplatin, and 12 months after the last dose of rituximab, 12 months after the final dose of epcoritamab and 3 months after the final dose of tocilizumab (as applicable), whichever is longer. Women must refrain from donating eggs during this same period. * Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices. * Hormonal contraceptive methods must be supplemented by a barrier method. * For male participants: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods, and agree to refrain from donating sperm, as defined below: * With a female partner of childbearing potential or pregnant female partners, male participants must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of \< 1% per year during the treatment period and for at least 12 months after the last dose of epcoritamab, 6 months after the last dose of oxaliplatin, 3 months after the last dose of gemcitabine, 12 months after the last dose of rituximab, or 2 months after the last dose of tocilizumab (as applicable), whichever is longer. Male participants must refrain from donating sperm during this same period. * If a female partner becomes pregnant or suspects becoming pregnant during treatment or within 12 months after the last dose of the trial intervention, the Investigator must be informed immediately. The Investigator may want to follow the pregnancy and may ask the female partner to sign a consent form so the Investigator or designee can collect information about the outcome of the pregnancy. * The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the individual. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not adequate methods of contraception. * Childbearing potential defined as not being permanently surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only). Per this definition, a female participant with tubal ligation is considered to be of childbearing potential. * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) * CONSOLIDATION WITH EPCORITAMAB: Achieved objective response per 2014 Lugano Classification at end of salvage * CONSOLIDATION WITH EPCORITAMAB: Absence of unrelated toxicity not present at baseline that might adversely affect participation/ administration of epcoritamab * CONSOLIDATION WITH EPCORITAMAB: Recovered from ASCT toxicities in patients who received ASCT. Including: outpatient status, able to drink and eat normally, and do not need intravenous hydration prior to cycle 1 day 1 of consolidation therapy * CONSOLIDATION WITH EPCORITAMAB: Will initiate treatment between day +30 and day +60 post-ASCT or post end of salvage therapy in those with CR/PR but do not proceed to ASCT * CONSOLIDATION WITH EPCORITAMAB: ECOG ≤ 2 within the screening period * CONSOLIDATION WITH EPCORITAMAB: ANC ≥ 1,000/mm\^3 within 14 days prior to day 1 of consolidation * CONSOLIDATION WITH EPCORITAMAB: Platelets ≥ 75,000/mm\^3 within 14 days prior to day 1 of consolidation * CONSOLIDATION WITH EPCORITAMAB: Total serum bilirubin ≤ 1.5X upper limit of normal (ULN), OR if Gilbert's disease: ≤ 3X ULN, within 14 days prior to day 1 of consolidation * CONSOLIDATION WITH EPCORITAMAB: AST ≤ 2.5 x ULN, OR if hepatic involvement by lymphoma: AST ≤ 5 x ULN, within 14 days prior to day 1 of consolidation * CONSOLIDATION WITH EPCORITAMAB: ALT ≤ 2.5 x ULN, OR If hepatic involvement by lymphoma: ALT ≤ 5 x ULN, within 14 days prior to day 1 of consolidation * CONSOLIDATION WITH EPCORITAMAB: Creatinine clearance of ≥ 40 mL/min within 14 days prior to day 1 of consolidation * CONSOLIDATION WITH EPCORITAMAB: No active ≥ grade 3 infection within 14 days prior to day 1 of consolidation * CONSOLIDATION WITH EPCORITAMAB: No other active malignancy requiring therapy. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy, or in situ cervical cancer * CONSOLIDATION WITH EPCORITAMAB: No symptomatic cardiac disease (including symptomatic ventricular dysfunction, symptomatic coronary artery disease, and symptomatic arrhythmias), cerebrovascular event/stroke or myocardial infarction within the last 6 months * CONSOLIDATION WITH EPCORITAMAB: No central nervous system involvement by lymphoma, including leptomeningeal involvement * CONSOLIDATION WITH EPCORITAMAB: No history of or current progressive multifocal leukoencephalopathy (PML) Exclusion Criteria: * Autologous or allogeneic stem cell transplant within 1 year prior to day 1 of study therapy * Chemotherapy, biological therapy, immunotherapy within 21 days or five half-lives (whichever is shorter for non-radiation therapy) prior to day 1 of study therapy other than a single cycle of R-GemOx * Has received or plans to receive radiotherapy except for palliative radiation to non-target lesions or major surgery within 4 weeks prior day 1 of study therapy * Prior solid organ transplantation * Vaccination with live vaccines within 4 weeks of the first dose of study drug or is expected to need any live vaccination during study participation including at least 3 months following the last dose of study treatment. * COVID-19 non-replicating adenoviral vaccines are permitted with a minimum period of 3 days between the vaccine and a dose of study treatment * Active medication use known to decrease T-cell numbers or activity or other concurrent immunosuppressive medication within 5 half-lives or 28 days, whichever is longer, prior to randomization except for up to 20 mg prednisone daily or equivalent * Known active central nervous system (CNS) involvement by lymphoma, including leptomeningeal involvement * Currently active, clinically significant cardiovascular disease, such as uncontrolled arrhythmia, or New York Heart Association (NYHA) heart failure class III-IV, or a history of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months of screening * Clinically significant liver disease, including active hepatitis, current alcohol abuse, or cirrhosis * History of severe allergic or anaphylactic reactions to anti CD20 monoclonal or bi-specific antibody therapy, or known significant allergy or intolerance to any component or excipient constituents of the study treatment (and their excipients) and/or other products in the same class * Clinically significant uncontrolled illness * Active uncontrolled infection requiring systemic antibiotics * Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) within 2 weeks prior to first dose of study treatment * Current seizure disorder requiring therapy * Peripheral (sensory) neuropathy grade \> 1 with the exception of neuropathy related directly to lymphoma (e.g., nerve compression from tumor) * Other active malignancy. 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 * Recent major surgery (within 4 weeks) prior to start of study therapy, other than for diagnosis * Known active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection. Patients with past HBV infection (defined as negative HBV surface antigen \[HBsAg\] and positive hepatitis B core antibody \[HBcAb\]) are eligible if HBV DNA is undetectable. Patients who are positive for HCV antibody are eligible if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA). Testing to be done only in patients suspected of having infections or exposures * Known active human immunodeficiency virus (HIV) infection. Subjects who have an undetectable or unquantifiable HIV viral load with CD4 \> 200 and are on highly active antiretroviral therapy (HAART) medication are allowed. Testing to be done only in patients suspected of having infections or exposures * Active (symptomatic) cytomegalovirus (CMV) disease * Active tuberculosis (TB) or history of completed treatment for active TB within the past 12 months * History of or current progressive multifocal leukoencephalopathy (PML) * Toxicities from prior anticancer therapy that have not resolved to Common Terminology Criteria for Adverse Events version 5.0 (CTCAE v5.0) grade 0 or 1, with the exception of alopecia * Females only: Pregnant or breastfeeding * Unable to tolerate SC injections * Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)