Inclusion Criteria for Phase Ib and Phase II Portions:

• Signed Informed Consent Form.
• Age ≥ 18 years at time of signing Informed Consent Form.
• Able to comply with the study protocol and procedures, in the investigator’s judgment.
• At least one bi-dimensionally measurable nodal lesion, defined as > 1.5 cm in its longest dimension, or one bi-dimensionally measurable extranodal lesion, defined as > 1.0 cm in its longest diameter.
• Confirmed availability of archival or freshly collected tumor tissue before study enrollment.
• Life expectancy of at least 24 weeks.
• Eastern Cooperative Oncology Group Performance Status of 0, 1, or 2.
• Left ventricular ejection fraction (LVEF) defined by multiple-gated acquisition (MUGA) scan or echocardiogram (ECHO) within the institutional limits of normal.
• Adequate hematologic function (unless inadequate function is due to underlying disease, as established by extensive bone marrow involvement, or is due to hypersplenism secondary to the involvement of the spleen by lymphoma per the investigator) defined as follows:
  • Hemoglobin ≥ 9 g/dL;
  • ANC ≥ 1.5 x 10^9/L;
  • Platelet count ≥ 75 x 10^9/L.

Serum creatinine ≥ ULN; or estimated creatinine clearance ≥ 50 mL/min by Cockroft-Gault method or other institutional standard methods, e.g. based on nuclear medicine renal scan

For women of childbearing potential: Agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating eggs, as defined below:

• 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, 12 months after the final dose of polatuzumab vedotin, 12 months after the final dose of rituximab, 12 months after the final dose of cyclophosphamide, doxorubicin, prednisone, or vincristine, and 3 months after the final dose of tocilizumab, as applicable. Women must refrain from donating eggs during this same period.
  • A woman is considered to be of childbearing potential if she is postmenarcheal, has not reached a postmenopausal state ( ≥ 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus);
  • Examples of contraceptive methods with a failure rate of < 1% per year include bilateral tubal ligation, male sterilization, established proper use of hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices. 
  • 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 patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or post-ovulation methods) and withdrawal are not acceptable methods of contraception.
• For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use a condom, and agreement to refrain from donating sperm, as defined below:
  • With female partners of childbearing potential or pregnant female partners, men must remain abstinent or use a condom during the treatment period and for 60 days after the final dose of mosunetuzumab, 6 months after the final dose of polatuzumab vedotin, 3 months after the final dose of rituximab, 6 months after the final dose of cyclophosphamide, doxorubicin, prednisone, or vincristine, and 60 days after the final dose of tocilizumab, as applicable, to avoid exposing the embryo. Men must refrain from donating sperm during this same period;
  • 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 patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or post-ovulation methods) and withdrawal are not acceptable methods of contraception.

Inclusion Criteria for Phase Ib Portion:

Participants must also meet the following criteria for study entry in the Phase Ib portion (Groups A and B):

• Histologically confirmed B-cell NHL according to WHO 2016 classification (pathology report must provide WHO 2016 diagnosis) expected to express the CD20 antigen (Swerdlow et al. 2016), except:
  • Plasma cell malignancies (e.g., lymphoplasmacytic lymphoma, Waldenström macroglobulinemia, plasmacytoma, plasmablastic lymphoma);
  • Primary DLBCL of the CNS;
  • Burkitt lymphoma.
• R/R B-cell NHL after at least one prior systemic lymphoma therapy.
• Treatment with at least one prior CD20-directed therapy (e.g., rituximab, obinutuzumab, ofatumumab, ibritumomab tiuxetan).
• Group B only: no prior treatment with polatuzumab vedotin.

Inclusion Criteria for Phase II Portion:

• Participants must also meet the following criteria for study entry in the Phase II portion: 
  • Previously untreated, histologically confirmed DLBCL according to WHO 2016 classification. 
  • Patients with a diagnosis of high-grade B-cell lymphoma (HGBL) with rearrangements of MYC and BCL2 and/or BCL6 or HGBL, not otherwise specified (NOS), are allowed.
• International Prognostic Index (IPI) score of 2−5.
• Ability and willingness to comply with the study protocol procedures, including PRO measures.

Exclusion Criteria:

• Pregnant or breastfeeding, or intending to become pregnant during the study or within 3 months after the final dose of mosunetuzumab, 12 months after the final dose of polatuzumab vedotin, 12 months after the final dose of rituximab, 12 months after the final dose of  cyclophosphamide, doxorubicin, prednisone, or vincristine, and 3 months after the final dose of tocilizumab, as applicable.
  • Women of childbearing potential must have a negative serum pregnancy test result within 7 days prior to initiation of study treatment.
• Prior treatment with mosunetuzumab. 
• Prior allogeneic stem-cell transplant.
• History of severe allergic or anaphylactic reactions to humanized or murine monoclonal antibodies or known sensitivity or allergy to murine products.
• Contraindication to receive full dose of any of the individual components of R-CHP.
• Contraindication to receive full dose of vincristine if planned study treatment includes vincristine (e.g., CHOP).
• Current Grade > 1 peripheral neuropathy.
• Patients with history of confirmed progressive multifocal leukoencephalopathy (PML).
• Known or suspected chronic active Epstein Barr virus (CAEBV) infection.
• Positive test results for chronic hepatitis B infection (defined as positive hepatitis B surface antigen [HBsAg] serology).
• Patients with occult or prior hepatitis B infection (defined as positive total hepatitis B core antibody and negative HBsAg) may be included if hepatitis B virus (HBV) DNA is undetectable at the time of screening. These patients must be willing to undergo monthly DNA testing and appropriate antiviral therapy as indicated.
• Acute or chronic hepatitis C virus (HCV) infection.
• Patients who are positive for HCV antibody must be negative for HCV by PCR.
• HIV seropositivity.
• Administration of a live, attenuated vaccine within 4 weeks before first study treatment administration or anticipation that such a live, attenuated vaccine will be required during the study.
• Prior solid organ transplantation.
• Known or suspected history of hemophagocytic lymphohistiocytosis
• 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 granulomatosis, Sjögren syndrome, Guillain-Barré syndrome, multiple sclerosis, vasculitis, or glomerulonephritis Patients with a history of autoimmune-related hypothyroidism on a stable dose of thyroid replacement hormone may be eligible.
• Received systemic immunosuppressive medications (including, but not limited to, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor agents) with the exception of pre-phase treatment with prednisone up to 100 mg daily for 7 days (or equivalent corticosteroid dose) prior to C1D1 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.
• Current or past history of CNS lymphoma.
• Current or past history of CNS disease, such as stroke, epilepsy, CNS vasculitis, or neurodegenerative disease.
• Patients with a history of stroke who have not experienced a stroke or transient ischemic attack in the past 2 years and have no residual neurologic deficits as judged by the investigator are allowed.
• Patients with a history of epilepsy who have had no seizures in the past 2 years while not receiving any anti-epileptic medications are allowed in the expansion cohorts only.
• Prior radiotherapy to the mediastinal/pericardial region.
• History of other malignancy that could affect compliance with the protocol or interpretation of results.
• Patients with a history of curatively treated basal or squamous cell carcinoma or melanoma of the skin or in situ carcinoma of the cervix are eligible.
• Patients with a malignancy that has been treated with curative intent will also be excluded unless the malignancy has been in documented remission without treatment for ≥ 2 years before enrollment.
• Evidence of significant, uncontrolled concomitant diseases that could affect compliance with the protocol or interpretation of results or that could increase risk to the patient, including renal disease that would preclude chemotherapy administration or pulmonary disease (including obstructive pulmonary disease and history of bronchospasm)
• Significant cardiovascular disease (such as New York Heart Association Class III or IV cardiac disease, congestive heart failure, myocardial infarction within the previous 6 months, unstable arrhythmias, or unstable angina) or significant pulmonary disease (including obstructive pulmonary disease and history of bronchospasm)
• History or presence of an abnormal ECG that is clinically significant in the investigator’s opinion, including complete left bundle branch block, second- or third-degree heart block, or evidence of prior myocardial infarction
• Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of 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 4 weeks before C1D1
• Clinically significant history of liver disease, including viral or other hepatitis, current alcohol abuse, or cirrhosis
• Recent major surgery within 4 weeks before the start of C1D1, other than superficial lymph node biopsies for diagnosis
• Any of the following abnormal laboratory values within 14 days of initiation of study treatment:
  • AST or ALT > 2.5 x ULN;
  • Total bilirubin ≥ 1.5 x ULN;
  • INR > 1.5 x ULN in the absence of therapeutic anticoagulation;
  • PTT or aPTT > 1.5 x ULN in the absence of a lupus anticoagulant.
• Any serious medical condition or abnormality in clinical laboratory tests that, in the investigator’s or Medical Monitor’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.

Exclusion Criteria for Phase Ib Portion:

Participants who also meet any of the following criteria will be excluded from study entry in the Phase Ib portion:

• Prior treatment with chemotherapy, immunotherapy, and biologic therapy 4 weeks prior to C1D1. 
• Prior treatment with radiotherapy within 2 weeks prior to C1D1.
• Adverse events from prior anti-cancer therapy resolved to ≤Grade 1 (with the exception of alopecia and anorexia).

Exclusion Criteria for Phase II Portion:

Participants who also meet any of the following criteria will be excluded from study entry in the Phase II portion: 

• Participants with transformed lymphoma.
• Prior therapy for B-cell NHL.