This phase I/II study is trying to understand how safe and effective treatment with a combination of targeted therapies (mosunetuzumab and tiragolumab), with or without immunotherapy (atezolizumab), is in people with relapsed or refractory diffuse large B-cell lymphoma or follicular lymphoma who have received some prior treatmentA Phase Ib/II Open-Label, Multicenter Study Evaluating the Safety, Efficacy, and Pharmacokinetics of Mosunetuzumab in Combination With Tiragolumab With or Without Atezolizumab in Patients With Relapsed or Refractory B-Cell Non-Hodgkin Lymphoma

Exclusion

• Received any of the following treatments prior to study entry: mosunetuzumab or other CD20/CD3-directed bispecific antibodies; tiragolumab or other anti-TIGIT agent; allogenic SCT; solid organ transplantation
• Currently eligible for autologous SCT
• Current or past history of 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)
• Contraindication to atezolizumab (if applicable) or tocilizumab
• Clinically significant toxicities from prior treatment have not resolved to Grade </= 1 (per NCI CTCAE v5.0) prior to the first study drug administration with exceptions defined by the protocol
• Treatment-emergent immune-mediated adverse events associated with prior immunotherapeutic agents as defined by the protocol
• Evidence of any significant, concomitant disease as defined by the protocol
• Major surgery within 4 weeks prior to first study treatment administration, with the exception of protocol-mandated procedures (e.g., tumor biopsies and bone marrow biopsies)
• Significant cardiac, pulmonary, CNS, or liver disease, or known active infections
• History of other malignancy that could affect compliance with the protocol or interpretation of results
• History of autoimmune disease with exceptions as defined in the protocol