A Study Evaluating the Safety, Pharmacokinetics, and Efficacy of Mosunetuzumab or Glofitamab in Combination With CC-220 and/or CC-99282 in Participants With B-Cell Non-Hodgkin Lymphoma

Inclusion Criteria: * Age \>/= 18 years * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0, 1, or 2 * History of one of the following histologically documented hematologic malignancies that are expected to express the CD20 antigen: In the Dose Escalation phase, participants must have relapsed after or failed to respond to at least two prior lines of systemic therapy. In the Dose Expansion phase, participants with FL Grades 1-3a must have relapsed after or failed to respond to at least one prior line of systemic therapy and must require systemic therapy. Participants with DLBCL/transformed FL must have relapsed after or failed to respond to at least one prior systemic treatment regimen. * Participants with DLBCL/transformed FL who have received only one prior line of therapy must: Not be considered a candidate for autologous stem cell transplantation (ASCT) due to age, performance status, comorbidities and/or insufficient response to prior treatment, or have refused ASCT; or be ineligible for or unable to receive chimeric antigen receptor T-cell (CAR-T) therapy due to reasons defined by the protocol * Fluorodeoxyglucose-avid lymphoma (i.e. PET-positive lymphoma) * At least one bi-dimensionally measurable nodal lesion (\> 1.5 cm in its largest dimension by diagnostic quality CT or PET/CT scan), or at least one bi-dimensionally measurable extranodal lesion (\> 1.0 cm in its largest dimension by diagnostic quality CT or PET/CT scan) * Availability of a representative tumor specimen and the corresponding pathology report for confirmation of the diagnosis of NHL * A fresh pretreatment biopsy during screening period, excisional or incisional, is preferred * Adequate hematologic function without growth factors or blood product transfusion within 14 days of first dose of study drug administration * Normal laboratory values * All participants and health care providers will be trained and counseled on pregnancy prevention. For female participants of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraception during the treatment period and for 3 months after the final dose of mosunetuzumab, at least 18 months after pre-treatment with obinutuzumab or 2 months after the last dose of glofitamab, 28 days after the last dose of CC-220, 28 days after the last dose of CC-99282, 3 months after the last dose of tocilizumab (if applicable), whichever is longer * For male participants: agreement to remain abstinent (refrain from heterosexual intercourse) or use a condom, and agree to refrain from donating sperm during the treatment period and for at least 3 months after pre-treatment with obinutuzumab or 2 months after the last dose of glofitamab, 28 days after the last dose of CC-220, 28 days after the last dose of CC- 99282, 2 months after the final dose of tocilizumab (if applicable), whichever is longer Exclusion Criteria: * Pregnancy or breastfeeding, or intention of becoming pregnant during the study (female participants of childbearing potential must have a negative serum pregancy test result within 14 days prior to initiation of the study treatment) or within 3 months after the final dose of mosunetuzumab, at least 3 months after pre-treatment with obinutuzumab or 2 months after the last dose of glofitamab, whichever is longer, 28 days after the last dose of CC-220, 28 days after the last dose of CC-9282, 3 months after the final dose of tocilizumab, whichever is longer * Participant has received prior therapy with cereblon (CRBN)-modulating drug (e.g., lenalidomide, avadomide/CC-122, pomalidomide) \</= 4 weeks prior to starting CC-220 and/or CC-99282 * Inability to swallow pills, or persistent diarrhea or malabsorption \>= Grade 2 National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE), despite medical management * QTc interval of \> 470 ms * The following treatments prior to study entry: mosunetuzumab, glofitamab, or other CD20/CD3-directed bispecific antibodies; allogenic stem cell therapy (SCT); solid organ transplantation * Treatments (investigational or approved) within the following time periods prior to initiation/first dose of study treatment: radiotherapy within 2 weeks; autologous SCT within 100 days; chimeric antigen receptor (CAR) T-cell therapy within 30 days; prior anti-lymphoma treatment with monoclonal antibodies or antibody-drug conjugates within 4 weeks; use of radioimmunoconjugates within 12 weeks; systemic immunosuppressive medications within 2 weeks; any other anti-cancer therapy, whether investigational or approved, including but not limited to chemotherapy, within 4 weeks or 5 half-lives of the drug, whichever is shorter * Live, attenuated vaccine within 4 weeks before first dose of study treatment, or in whom it is anticipated that such a live attenuated vaccine will be required during the study period or within 5 months after the final dose of study treatment * Current or past history of central nervous system (CNS) lymphoma or leptomeningeal infiltration * History of severe allergic or anaphylactic reactions to humanized or murine monoclonal antibody therapy (or recombinant antibody-related fusion proteins) * 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, granulomatosis with polyangiitis, Sjögren's syndrome, Guillain-Barré syndrome, multiple sclerosis, vasculitis, or glomerulonephritis * Major surgery or significant traumatic injury \< 28 days prior to enrollment (excluding biopsies) or anticipation of the need for major surgery during study treatment * Clinically significant toxicities from prior treatment have not resolved to Grade \</= 1 (per US national cancer institute (NCI) common terminology criteria for adverse events (CTCAE) v5.0) prior to the first study drug administration with exceptions defined by the protocol * Evidence of any significant, concomitant disease (e.g. cardiovascular, pulmonary, liver, CVA or stroke, ILD, PML, infection, HLH etc) that could affect compliance with the protocol or interpretation of results * For participants enrolled into glofitamab cohort: documented refractoriness to an obinutuzumab monotherapy-containing regimen (defined as disease that did not achieve response (PR or CR) or progressed within 6 months of the last dose of an obinutuzumab-containing regimen)