• Documented informed consent of the participant and/or legally authorized representative

‣ Assent, when appropriate, will be obtained per institutional guidelines

• Be willing to provide tissue from a fresh core or excisional biopsy (performed as standard of care) of a tumor lesion prior to starting study therapy or from diagnostic tumor biopsies

‣ If unavailable, exceptions may be granted with study principal investigator (PI) approval

• Age: ≥ 18 years

• Eastern Cooperative Oncology Group (ECOG) ≤ 2

• Histologically confirmed diagnosis of follicular lymphoma grade 1-3a according to the World Health Organization (WHO) classification. Note: A history of diffuse large B-cell lymphoma (DLBCL) and/or grade 3b follicular lymphoma is allowed (follicular large B-cell lymphoma in the WHO 5th classification of mature B-cell lymphoma) but these cannot be present at the time of study enrollment. Enrollment of any such cases on this study must receive prior approval by the study PI

• Relapsed/ refractory disease after at least one prior line of therapy. Relapse must have been confirmed histologically

• Tumor must be positive for CD20 by immunohistochemistry or flow cytometry after the most recent therapy. Note: As a pan-B marker, CD79B+ is nearly always present and is not a criterion for inclusion

• Active disease requiring treatment per treating physician's decision

• Radiographically measurable disease by Lugano criteria (e.g., one or more nodal sites of disease ≥ 1.5 cm and/or at least one extranodal site of disease ≥ 1.0 cm in longest dimension)

• Fully recovered from the acute toxic effects (except alopecia) to ≤ grade 1 to prior anti-cancer therapy

• WITHOUT BONE MARROW INVOLVEMENT BY LYMPHOMA: Absolute neutrophil count (ANC) ≥ 1,000/mm\^3. NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement

• WITH BONE MARROW INVOLVEMENT BY LYMPHOMA AND/OR DISEASE-RELATED NEUTROPENIAS: ANC ≥ 500/mm\^3. NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement

• WITHOUT BONE MARROW INVOLVEMENT BY LYMPHOMA: Platelets ≥ 75,000/mm\^3. NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement

• WITH BONE MARROW INVOLVEMENT BY LYMPHOMA AND/OR DISEASE-RELATED CYTOPENIAS: Platelets ≥ 50,000/mm\^3. NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement

• Hemoglobin ≥ 8 g/dL. NOTE: Red blood cell transfusions are not permitted within 7 days of hemoglobin assessment unless cytopenia is secondary to disease involvement

• Total bilirubin ≤ 1.5 x upper limit of normal (ULN). If hepatic involvement by lymphoma, or Gilbert's disease: ≤ 3 x ULN

• Aspartate aminotransferase (AST) ≤ 2.5 x ULN. If hepatic involvement by lymphoma: AST ≤ 5 x ULN

• Alanine aminotransferase (ALT) ≤ 2.5 x ULN. If hepatic involvement by lymphoma: ALT ≤ 5 x ULN

• Creatinine clearance of ≥ 40 mL/min per 24 hour urine test or the Cockcroft-Gault formula

• IF NOT RECEIVING ANTICOAGULANTS: International normalized ratio (INR) OR prothrombin (PT) ≤ 1.5 x ULN

• IF ON ANTICOAGULANT THERAPY: PT must be within therapeutic range of intended use of anticoagulants

• IF NOT RECEIVING ANTICOAGULANTS: Activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN

• IF ON ANTICOAGULANT THERAPY: aPTT must be within therapeutic range of intended use of anticoagulants

• WOMEN OF CHILDBEARING POTENTIAL (WOCBP): Negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required

• Agreement by females of childbearing potential to abstain from heterosexual intercourse or use two adequate method of birth control, including at least 1 method with a failure rate of \< 1% per year, for at least 28 days prior to day 1 of cycle 1, during the treatment period (including periods of treatment interruption), until 3 months after the final dose mosunetuzumab, 3 months after the last dose of polatuzumab vedotin, and 3 months after the last dose of tocilizumab (if applicable). Women must refrain from donating eggs during this same period. Agreement by males to abstain from heterosexual intercourse or use a condom with female partners of childbearing potential or pregnant female partners during the treatment period and until 5 months after the last dose of polatuzumab vedotin, and 2 months after the last dose of tocilizumab (if applicable). Men must refrain from donating sperm during this same period

‣ Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) with no identified cause other than menopause

⁃ 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