Inclusion Criteria:  Eastern Cooperative Oncology Group (ECOG) Performance Status of 0, 1, or 2 Life expectancy of at least 12 weeks CD20+ aggressive lymphoma as determined by the local hemopathology laboratory from the following diagnoses by 2016 World Health Organization classification of lymphoid neoplasms: DLBCL, not otherwise specified (NOS); high-grade B-cell lymphoma (NOS or double/triple hit); trFL R/R to standard therapies to trFL; FL3B Received at least one prior systemic therapy for aggressive non-Hodgkin's lymphoma (aNHL) Have either relapsed or have become refractory to a prior regimen must meet the following criteria: relapsed to prior regimen(s) after having a documented history of response (CR or PR) of at least 6 months in duration from completion of regimen(s); refractory to any prior regimen, defined as no response to the prior therapy, or progression within 6 months of completion of the last dose of therapy Participants who have received only one prior line of therapy must be ineligible for autologous stem cell transplant (ASCT) Measurable disease, defined as at least 1 bi-dimensionally measurable nodal lesion, defined as > 1.5 cm in its longest dimension, or at least 1 bi-dimensionally measurable extra nodal lesion, defined as > 1.0 cm in its longest dimension Have a pathology report for the initial histopathology diagnosis and the most recent histopathology diagnosis prior to entering the study Representative tumor specimen and the corresponding pathology report available for confirmation of diagnosis as well as for biomarker analysis Adequate hepatic, hematologic, and renal function  Exclusion Criteria:  Pregnant or breast feeding, or intending to become pregnant during the study or within 3 months after the final dose of mosunetuzumab, 9 months after the final dose of polatuzumab vedotin, 12 months after the final dose of rituximab, 6 months after the final dose of gemcitabine, 9 months after the final dose of oxaliplatin, and 3 months after the final dose of tocilizumab, as applicable Inability to comply with protocol-mandated activity restrictions Prior treatment with mosunetuzumab or other CD-20-directed bispecific antibodies, polatuzumab vedotin, or R-GemOx or Gem-Ox Contraindication to any component of the study treatment Grade > 1 peripheral neuropathy Received anti-lymphoma treatments with monoclonal antibodies, radio-immunoconjugates or antibody-drug conjugates (ADCs) within 4 weeks before the first dose of study treatment Treatment with any chemotherapeutic agent, or treatment with any other anti-cancer agent (investigational or otherwise) within 4 weeks or 5 half-lives of the drug, whichever is shorter, prior to the first dose of study treatment Treatment with radiotherapy within 2 weeks prior to the first dose of study treatment ASCT within 100 days prior to the first study treatment administration Prior treatment with chimeric antigen receptor (CAR) T cell therapy within 30 days before the first study treatment administration Prior allogenic stem cell transplant (SCT) Have had a solid organ transplantation Known or suspected history of hemophagocytic lymphohistiocytosis (HLH) History of confirmed progressive multifocal leukoencephalopathy History of severe allergic or anaphylactic reactions to monoclonal antibody therapy (or recombination antibody-related fusion proteins) History of malignancy that has been treated with curative intent within >/= 2 years prior to screening, with the exception of the cancer under investigation in this study and malignancies with a negligible risk of metastasis or death (e.. 5-year overall survival rate > 90%), such as adequately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, localized prostate cancer, ductal carcinoma in situ, or Stage 1 uterine cancer Currently have or have had a past history of central nervous system (CNS) involvement of lymphoma History of CNS disease which was symptomatic or required treatment in the past 1 year, such as stroke, epilepsy, CNS vasculitis, or neurodegenerative disease Significant cardiovascular disease such as New York Heart Association Class III or IV cardiac disease, myocardial infarction within the last 6 months, unstable arrhythmias, or unstable angina Significant active pulmonary disease Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of the nail beds) at study enrollment, or any major episode of infection requiring treatment with IV antibiotics or hospitalization (relating to the completion of the course of antibiotics) within 2 weeks prior to the first study treatment administration Known or suspected chronic active Epstein-Barr virus (EBV) infection Recent major surgery within 4 weeks prior to the first study treatment administration Positive test results for chronic hepatitis B infection Acute or chronic hepatitis C virus (HCV) infection History of HIV infection Have been administered a live, attenuated vaccine within 4 weeks before the first dose of study treatment administration or anticipation that such a live, attenuated vaccine will be required during the study History of autoimmune disease Received systemic immunosuppressive medications (including, but not limited to cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-TNF agents) with the exception of corticosteroid treatment </= 10 mg/day prednisone or equivalent within 2 weeks prior to first dose of study treatment Received investigational therapy, whether or not intended for lymphoma treatment, within 7 days prior to initiation of study treatment Clinically significant history of liver disease, including viral or other hepatitis, or cirrhosis Any serious medical condition or abnormality in clinical laboratory tests that precludes the participant's safe participation in and in the completion of the study, or which could affect compliance with the protocol or interpretation of results