Testing the Addition of an Anti-Cancer Drug, Glofitamab, to the Usual Chemotherapy Treatment (Alternating R-CHOP/R-DHAP) for Previously Untreated Mantle Cell Lymphoma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed previously untreated mantle cell lymphoma which is stage II bulky, stage III, or stage IV and fit for intensive chemotherapy. TP53 mutated patients are eligible * Patients must exhibit measurable disease by PET or CT imaging with at least one site of disease \> 1.5 cm in longest dimension or documented bone marrow involvement * Age ≥ 18 years to ≤ 75 years. Because no dosing or adverse event data are currently available on the use of glofitamab in combination with R-CHOP/R-DHAP 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 ≥ 1,000/mcL * Platelets ≥ 100,000/mcL * Total bilirubin ≤ 2 × institutional upper limit of normal (ULN) unless total bilirubin elevation is attributable to Gilbert's syndrome or lymphomatous infiltration of the liver in whom total bilirubin must be \< 3 times ULN * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/ alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 × institutional ULN * Creatinine clearance ≥ 30 ml/min * Left ventricular ejection fraction ≥ 45% by echocardiogram or Multiple-Gated Acquisition (MUGA) scan * International Normalized Ratio (INR) or prothrombin time (PT) ≤ 1.5 × ULN in the absence of therapeutic anticoagulation * Partial thromboplastin time (PTT) or activated partial thromboplastin time (aPTT) ≤ 1.5 × ULN in the absence of a lupus anticoagulant * Hemoglobin (Hgb) ≥ 8 g/dL * 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 new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of therapy * 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 with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class II or better * The effects of glofitamab on the developing human fetus are unknown. For this reason and because glofitamab used in this trial is known to be teratogenic, women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and 2 months after completion of glofitamab administration and 12 months after completion of rituximab administration. 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. Male participants with a female partner of childbearing potential or pregnant female partners 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 2 months after the final dose of glofitamab or 160 days after the final dose of rituximab. Male participants must refrain from donating sperm during this same period * Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants Exclusion Criteria: * Patients who received prior treatment for MCL, including chemotherapy, bispecific antibody therapy, or other cytotoxic or cellular therapy including autologous hematopoietic stem cell transplant (autoHCT). Since this study aims to evaluate safety and efficacy in previously untreated patients by using this regimen as a first-line therapy, prior systemic therapy would potentially bias and affect endpoints and results * Patients who have not recovered from AEs 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 lymphoma that shows active and uncontrolled CNS involvement; uncontrolled CNS involvement may require different systemic therapy in addition to CNS directed therapy, which would interfere with the study regimen and sequence of drug administration * History of allergic reactions attributed to compounds of similar chemical or biologic composition to glofitamab or other agents used in study * Patients with active, uncontrolled infection defined as ongoing signs or symptoms of infection despite antimicrobial therapy or other infection-directed therapy * Patients with uncontrolled intercurrent illness or any other significant condition(s) that would make this protocol unreasonably hazardous * Pregnant women are excluded from this study because glofitamab is an agent 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 glofitamab, breastfeeding should be discontinued if the mother is treated with glofitamab. These potential risks may also apply to other agents used in this study * Patients with prior solid organ transplantation * Prior treatment with systemic immunotherapeutic agents, including but not limited to, radio-immuno-conjugates, antibody-drug conjugates, immune/cytokines and monoclonal antibodies (mAbs) (e.g., anticytotoxic T lymphocyte associated protein 4, anti-PD-1, and anti-PD-L1) within 4 weeks or five half-lives of the drug, whichever is shorter * Prior use of any monoclonal antibody for the purposes of treating cancer within 3 months of the start of cycle 1 * Any investigational therapy for the purposes of treating cancer within 28 days prior to the start of cycle 1 * Prior radiotherapy to the mediastinal/pericardial region. Radiotherapy to non-target lesion sites will be permitted * Corticosteroid use \> 50 mg/day of prednisone or equivalent, for purposes other than lymphoma symptom control. * Participants receiving corticosteroid treatment with ≤ 50 mg/day of prednisone or equivalent for reasons other than lymphoma symptom control (e.g., rheumatoid arthritis) must be documented to be on a stable dose of at least 4 weeks duration prior to the start of cycle 1. * Corticosteroid therapy for control of cancer symptoms or side effects of prior treatment (e.g., nausea or B-symptoms) is permitted. * The use of inhaled corticosteroids is permitted. * The use of mineralocorticoids for management of orthostatic hypotension is permitted. * The use of physiologic doses of corticosteroids for management of adrenal insufficiency is permitted. * Participants who require lymphoma symptom control during screening may receive steroids in the following manner: * Up to 50 mg/day of prednisone or equivalent may be used for lymphoma symptom control during screening, including prior to finalization of staging (not included as part of pre-phase treatment). * If glucocorticoid treatment is urgently required at higher doses for lymphoma symptom control prior to the start of study treatment, tumor assessments must be completed prior to initiation of \>30-100 mg/day of prednisone or equivalent. Prednisone \> 30-100 mg/day or equivalent may be given for a maximum of 10-14 days as a pre-phase treatment. As part of the pre-phase treatment, vincristine may not be administered * Patients who had a recent major surgery (within 4 weeks prior to the start of cycle 1), other than for diagnosis * Patients with known or suspected history of hemophagocytic lymphohistiocytosis (HLH) * Patients with current or past history of Waldenström macroglobulinemia * Patients with known or suspected active infection, or reactivation of a latent infection, whether bacterial, viral (including, but not limited to, SARS-Cov-2, Epstein Barr virus \[EBV\], known or suspected chronic active EBV \[CAEBV\], cytomegalovirus \[CMV\]), fungal, mycobacterial, or other pathogens (excluding fungal infections of nail beds) or any major episode of infection requiring hospitalization or treatment with IV antibiotics (for IV antibiotics this pertains to completion of last course of antibiotic treatment) within 4 weeks of dosing * History of treatment-emergent immune-related adverse events associated with prior immunotherapeutic agents, as follows: * Grade ≥ 3 adverse events with the exception of Grade 3 endocrinopathy managed with replacement therapy. * Grade 1-2 adverse events that did not resolve to baseline after treatment discontinuation * History of autoimmune disease, including but not limited to myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjögren's syndrome, Guillain-Barré syndrome, multiple sclerosis, vasculitis, or glomerulonephritis. * Participants with autoimmune disease that is controlled or not currently active (i.e., distant history of Guillain-Barré syndrome that has resolved) may be eligible for this study. * Participants with a history of autoimmune-related hypothyroidism on a stable dose of thyroid replacement hormone may be eligible for this study. * Participants with a history of disease-related immune thrombocytopenic purpura or autoimmune hemolytic anemia may be eligible for this study. * Participants with controlled Type I diabetes mellitus who are on an insulin regimen are eligible for the study * • Participants with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only are eligible (e.g., participants with psoriatic arthritis are excluded) if all the following conditions are met: * Rash covers \< 10% of body surface area. * Disease is well controlled for the last 12 months and requires only low potency topical corticosteroids * Patients with clinically significant liver disease, including active viral or other hepatitis or cirrhosis * Live, attenuated vaccine within 4 weeks before study treatment infusion on day 1 of cycle 1 or anticipation that such a live, attenuated vaccine will be required during the study. Live vaccines during the study and until participants B cells recover, are prohibited. Influenza vaccination should be given during influenza season only. Participants must not receive live, attenuated influenza vaccine at any time during the study treatment period * Patients with suspected active or latent tuberculosis (as confirmed by a positive interferon gamma release assay * Patients with a history of progressive multifocal leukoencephalopathy