Mosunetuzumab in Combination With Platinum-Based Salvage Chemotherapy in Patients With Relapsed/Refractory Aggressive B Cell Lymphoma

Inclusion Criteria: * Diagnosis of large, high-grade, or transformed B cell lymphoma or follicular lymphoma grade 3B that is refractory to or has relapsed after anti-CD20 mAb plus anthracycline-containing combination chemotherapy. A biopsy immediately prior to enrollment is not mandatory. * Must have received at least one prior line of systemic treatment containing conventional cytotoxic chemotherapy for lymphoma. Conventional cytotoxic chemotherapy with or without an anti-CD20 mAb for prior/underlying indolent NHL (with or without maintenance/extended-use anti-CD20 mAb) will count as one line of systemic therapy. * At least 18 years of age. * ECOG performance status ≤ 2 * Adequate hematologic function (unless due to underlying lymphoma per the investigator), defined as follows: * Absolute neutrophil count ≥ 1,000/mcL * Platelets ≥ 75,000/mcL without platelet transfusion within 14 days prior to the first dose of mosunetuzumab * Hemoglobin ≥ 8 g/dL without red blood cell transfusion within 7 days prior to the first dose of mosunetuzumab * Patients with extensive bone marrow involvement by lymphoma and/or disease-related cytopenias (e.g., immune thrombocytopenia) may be enrolled if the following criteria are met: * Absolute neutrophil count ≥ 500/mcL * Platelet count ≥ 50,000/mcL without platelet transfusion within 14 days prior to the first dose of mosunetuzumab * No red blood cell transfusion within 7 days prior to the first dose of mosunetuzumab * Normal laboratory values: * Serum total bilirubin ≤ 1.5 x IULN (or ≤ 3 x IULN for patients with Gilbert's syndrome) * AST(SGOT)/ALT(SGPT) ≤ 3.0 x IULN * Serum creatinine ≤ 1.5 x IULN or creatinine clearance ≥ 50 mL/min by Cockcroft-Gault * The effects of mosunetuzumab on the developing human fetus are unknown. For this reason, women of childbearing potential and men must agree to use adequate contraception (as defined in protocol) prior to study entry, for the duration of study treatment, and for 3 months following the final dose of mosunetuzumab. Specifically, women must remain abstinent or use contraceptive methods with a failure rate of \<1% per year during the treatment period and for 3 months after the final dose of mosunetuzumab as applicable. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. Men treated or enrolled on this protocol with a female partner of childbearing potential or pregnant female partner must also agree to use adequate contraception prior to the study, for the duration of study treatment, and for 3 months following the final dose of mosunetuzumab. * Ability to understand and willingness to sign an IRB approved written informed consent document. Exclusion Criteria: * Known history of treatment-emergent immune-related adverse events associated with prior immunotherapeutic agents. * Known history of macrophage activation syndrome (MAS) or hemophagocytic lymphohistiocytosis (HLH). * Prior allogeneic stem cell transplant. * Treatment with radiotherapy within 2 weeks prior to the first dose of mosunetuzumab (otherwise one measurable lesion outside of the radiation field must remain). * Prior treatment with CAR-T cell therapy within 30 days of first dose of mosunetuzumab. * Any history of lymphomatous involvement of the CNS. Note: If CSF studies via lumbar puncture and/or neuroimaging are performed per physician discretion to rule out CNS involvement given active CNS signs or symptoms, these assessments should be completed within 6 weeks prior to study enrollment. There are no restrictions on the timing of CSF studies via lumbar puncture and/or neuroimaging performed for routine staging of patients without CNS signs or symptoms, or if performed for reasons unrelated to lymphoma evaluation. * Current or recent history (within the last 6 months) of clinically relevant CNS disease or pathology, such as stroke, epilepsy, CNS vasculitis, or neurodegenerative disease. * Clinically significant toxicity (other than alopecia) from prior treatment that has not resolved to grade ≤ 1 per NCI CTCAE v 5.0 prior to Day 1 of Cycle 1. * Treatment with systemic immunosuppressive medications, including but not limited to prednisone (\> 20 mg), azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor agents within 2 weeks prior to Day 1 of Cycle 1. Note: The use of inhaled corticosteroids, mineralocorticoids for management of orthostatic hypotension, and single dose dexamethasone for nausea or B symptoms is permitted. * History of solid organ transplantation. * History of severe allergic or anaphylactic reaction to humanized, chimeric, or murine monoclonal antibodies (mAbs). * Known hypersensitivity to biopharmaceuticals produced in CHO cells or any component of the mosunetuzumab formulation, including mannitol. * History of erythema multiforme, grade ≥ 3 rash, or blistering following prior treatment with immunomodulatory derivatives. * Known active bacterial, viral, fungal, or other infection, or any major episode of infection requiring treatment with IV antibiotics within 1 week of Day 1 of Cycle 1. * Known or suspected chronic active Epstein-Barr virus (EBV) infection. * Clinically significant history of liver disease, including viral or other hepatitis, or cirrhosis. * Active hepatitis B infection: \*Patients who are hepatitis B surface antigen (HBsAg) negative and hepatitis B core antibody (HBcAb) positive must be negative for hepatitis B virus (HBV) polymerase chain reaction (PCR) to be eligible for study participation. * Active hepatitis C infection: \*Patients who are positive for hepatitis C virus (HCV) antibody must be negative for HCV by PCR to be eligible for study participation. * Known history of human immunodeficiency virus (HIV) positive status. * History of progressive multifocal leukoencephalopathy (PML). * Administration of a live, attenuated vaccine within 4 weeks before first dose of study treatment or anticipation that such a live attenuated vaccine will be required during the study: * Patients must not receive live, attenuated vaccines (e.g., FluMist®) while receiving study treatment or after the last dose until B cell recovery to the normal ranges. * Other malignancy that could affect compliance with the protocol or interpretation of results, with the exception of the following: * Any of the following malignancies previously curatively treated: carcinoma in situ of the cervix, good-prognosis ductal carcinoma in situ of the breast, basal or squamous cell skin cancer. * Stage I melanoma, low grade, early stage localized prostate cancer, or any other previously treated malignancy that has been in remission without treatment for \>2 years prior to enrollment. * Active autoimmune disease requiring treatment. * History of autoimmune disease, including, but not limited to, myocarditis, interstitial lung disease (idiopathic, autoimmune, or drug-induced), pneumonitis (autoimmune or drug-induced), 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: * Patients with a remote history of, or well-controlled autoimmune disease, with a treatment-free interval from immunosuppressive therapy for 12 months may be eligible to enroll if judged to be safe by the investigator. * Patients with a history of autoimmune-related hypothyroidism on a stable dose of thyroid-replacement hormone are eligible. * Patients with controlled Type 1 diabetes mellitus who are on an insulin regimen are eligible for the study. * Patients with a history of disease-related immune thrombocytopenic purpura, or autoimmune hemolytic anemia may be eligible. * Evidence of any significant, uncontrolled concomitant disease that could affect compliance with the protocol or interpretation of results, including, but not limited to, significant cardiovascular disease (e.g., New York Heart Association Class III or IV cardiac disease, myocardial infarction within the previous 6 months, unstable arrhythmia, or unstable angina) or significant pulmonary disease (such as obstructive pulmonary disease or history of bronchospasm). * Major surgical procedure other than for diagnosis within 28 days prior to Cycle 1 Day 1 or anticipation of a major surgical procedure during the study. * Pregnant or lactating or intending to become pregnant during the study: \*Women of childbearing potential must have one negative serum pregnancy test result (minimum sensitivity, 25 mIU/mL) within seven days of Cycle 1 Day 1. * Any serious medical condition or abnormality in clinical laboratory tests that, in the investigator's judgment, precludes the patient's safe participation in and completion of the study, or which could affect compliance with the protocol or interpretation of results.