Mosunetuzumab Consolidation Therapy After autoSCT in r/r Aggressive B Cell Lymphoma

Inclusion Criteria for Screening Pre-autoSCT: * Diagnosis of rCD20+ large B cell lymphoma, high-grade B cell lymphoma, transformed B cell lymphoma, primary mediastinal B cell lymphoma, or follicular lymphoma grade 3B. * Planning to undergo autologous stem cell transplantation after two or more prior lines of therapy for lymphoma, including treatment for prior/underlying indolent B-NHL. * At least 18 years of age. * ECOG performance status ≤ 2 * 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 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 for Screening Pre-autoSCT: * Chemotherapy-resistant (stable or progressive disease) lymphoma at pre-autoSCT response assessment to salvage therapy. * Known history of grade 3+ treatment-emergent immune-related adverse events associated with prior immunotherapeutic agents. * Known history of macrophage activation syndrome (MAS) or hemophagocytic lymphohistiocytosis (HLH) if unrelated to prior lymphoma. If patient has a history of HLH secondary to prior lymphoma, all signs and symptoms of HLH secondary to prior lymphoma must be resolved for patient to be eligible for the study. * 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. * Prior allogeneic stem cell transplant. * 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, including mannitol. * History of erythema multiforme, grade ≥ 3 rash, or blistering following prior treatment with immunomodulatory derivatives. * 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 (Anti-HBc) 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). * 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, pneumonitis, 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). * 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 enrollment. Inclusion Criteria for Screening Post-autoSCT: * Diagnosis of CD20+large B cell lymphoma, high-grade B cell lymphoma, transformed B cell lymphoma, primary mediastinal B cell lymphoma, or follicular lymphoma grade 3B. * Status post autologous stem cell transplantation after two or more prior lines of therapy for lymphoma, including treatment for prior/underlying indolent B-NHL. * At least 18 years of age. * ECOG performance status ≤ 2 (see Appendix A) * 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 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. * Adequate hematologic function defined as follows: * Absolute neutrophil count ≥ 1,000/mcL without G-CSF use in past 7 days * Platelets ≥ 75,000/mcL without TPO mimetic use in past 7 days * Hemoglobin ≥ 8 g/dL without red blood cell transfusion in past 7 days * Normal laboratory values: * Serum total bilirubin ≤ 1.5 x IULN (or ≤ 3 x IULN for patients with Gilbert syndrome) * AST(SGOT)/ALT(SGPT) ≤ 2.5 x IULN * Measured or estimated creatinine clearance ≥ 50 mL/min by Cockcroft-Gault * Ability to understand and willingness to sign an IRB approved written informed consent document. Exclusion Criteria for Rescreening (post-autoSCT): * Clinical evidence of progressive lymphoma after auto-SCT. * 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. * 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. * 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. * Major surgical procedure other than for diagnosis within 28 days prior to Day 1 of Cycle 1 Day 1 or anticipation of a major surgical procedure during the course of the study. * Any signs or symptoms of HLH secondary to lymphoma within 60 days prior to Day 1 of Cycle 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. * Known history of grade 3+ treatment-emergent immune-related adverse events associated with prior immunotherapeutic agents. * Known history of macrophage activation syndrome (MAS) or hemophagocytic lymphohistiocytosis (HLH) if unrelated to prior lymphoma. If patient has a history of HLH secondary to prior lymphoma, all signs and symptoms of HLH secondary to prior lymphoma must be resolved for patient to be eligible for the study. * 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. * Prior allogeneic stem cell transplant. * 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, including mannitol. * History of erythema multiforme, grade ≥ 3 rash, or blistering following prior treatment with immunomodulatory derivatives. * 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 (Anti-HBc) 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). * 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, pneumonitis, 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). * 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 enrollment.