S2114: Therapy Following CAR-T (Diffuse Large B-cell Lymphoma or Grade IIIB Follicular Lymphoma)

If you choose to join this study, you will get a random assignment (fair, equal chance) to 1 of 4 groups: - If you are in Group 1, you will get the study drug mosunetuzumab through a vein in your arm for 8 cycles of treatment. Each cycle is 21 days, or up to 28 days if you need more recovery time between treatments. In cycle 1, you will get this drug on days 1, 8, and 15. First, you will get the pre-medication, dexamethasone. Thirty minutes later, you will get two other pre-medications called acetaminophen and diphenhydramine. One hour after the dexamethasone was given, you will get mosunetuzumab. For cycles 2 through 8, you will only get mosunetuzumab on day 1 of each cycle and not on days 8 and 15. You will get all the pre-medications during cycles 1 and 2. During cycles 3 through 8, you will only receive the pre-medications, acetaminophen and diphenhydramine, unless your study doctor thinks you should continue the dexamethasone. - If you are in Group 2, you will get the study drug polatuzumab vedotin through a vein in your arm on day 1 of each cycle for 6 cycles of treatment. Each cycle is 21 days. - If you are in Group 3, you will get both study drugs (mosunetuzumab, and polatuzumab vedotin) through a vein in the arm for up to 8 cycles of treatment. Each cycle is 21 days. In cycle 1, you will receive mosunetuzumab on days 1, 8, and 15. First, you will get the pre-medication, dexamethasone. Thirty minutes later, you will get two other pre-medications called acetaminophen and diphenhydramine. One hour after the dexamethasone was given, you will get mosunetuzumab. In cycles 2 through 7, you will receive mosunetuzumab, and polatuzumab vedotin on day 1. In cycle 8, you will receive mosunetuzumab day 1. During cycles 3 through 8, you will only receive the pre-medications, acetaminophen and diphenhydramine, unless your study doctor thinks you should continue the dexamethasone. - If you are in Group 4, you will not get any study drugs. You will not receive any treatment after CAR T-cell therapy. The study doctors will closely watch your condition. You will have the option to join Group 3 if your cancer gets worse within 12 months after CAR T-Cell therapy.