PRIMARY OBJECTIVE:~I. To determine the safety and tolerability of maintenance acalabrutinib following cellular therapy in participants with large B-cell lymphoma at very high risk for relapse.~SECONDARY OBJECTIVES:~I. To estimate the effectiveness of maintenance acalabrutinib following cellular therapy in participants with large B-cell lymphoma at high risk for relapse.~II. To estimate the durability of remission after completion of acalabrutinib maintenance.~III. To estimate survival following completion of acalabrutinib maintenance. IV. To estimate the rate of conversion from partial response (PR) following chimeric antigen receptor (CAR) T-cell therapy to complete response (CR) after the addition of acalabrutinib maintenance.~V. To estimate rates of dose reductions, dose pauses, and permanent discontinuations of acalabrutinib that occur post-cellular therapy.~VI. To estimate the rate of stage >= 2 graft-versus-host disease in participants receiving acalabrutinib post-allogeneic hematopoietic cell transplantation (alloHCT).~VII. To estimate the rates of grade 2, 3, and 4 hematologic toxicity in participants receiving acalabrutinib post-cellular therapy.~VIII. To estimate the rates of grade 2, 3, and 4 non-hematologic toxicity in participants receiving acalabrutinib post-cellular therapy.~EXPLORATORY OBJECTIVES:~I. To evaluate CAR T-cell persistence in the setting of acalabrutinib. II. To evaluate changes in immunophenotype of peripheral blood mononuclear cells before and after initiation of acalabrutinib, and changes at time of relapse.~III. To evaluate changes in circulating tumor deoxyribonucleic acid (ctDNA), intracellular cytokine and phospho-protein profiling of peripheral blood mononuclear cells before and after initiation of acalabrutinib, and changes at time of relapse.~IV. To determine if there are signs of central nervous system (CNS) penetration of acalabrutinib.~OUTLINE: Patients are assigned to 1 of 3 groups.~GROUP I (ALLOHCT GROUP): Beginning day 90, patients receive acalabrutinib orally (PO) once daily (QD) and then( orally, twice daily (PO BID) once no longer on prophylactic antifungal (CYP34A inhibitors) until day 365 in the absence of disease progression or unacceptable toxicity.~GROUP II (AUTOLOGOUS STEM CELL TRANSPLANTATION [ASCT] GROUP): Beginning day 60, patients receive acalabrutinib PO QD and then PO BID from day 74 if there are no dose reductions until day 365 in the absence of disease progression or unacceptable toxicity.~GROUP III (CAR-T CELL THERAPY GROUP): Beginning anytime between days 28-104, patients receive acalabrutinib PO BID until day 365 in the absence of disease progression or unacceptable toxicity.~After completion of study treatment, patients are followed up at 30 days.
This phase Ib/II trial studies the side effects and efficacy of maintenance acalabrutinib following cellular therapy in treating patients with large B-cell lymphoma at very high risk of the cancer coming back. Acalabrutinib is a small molecular inhibitor that may interfere with the ability of cancer cells to grow and spread.