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.

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.

Inclusion Criteria:

• Ages 18-70 years

• One of the following:

  • Patients undergoing autologous stem cell transplantation (ASCT) or any Food and Drug Administration (FDA)-approved chimeric antigen receptor (CAR) T-cell therapy product for:

    • High grade B-cell lymphoma (double or triple hit) with rearrangements in bcl-2 and/or bcl-6, and rearrangement in myc
    • Large B-cell lymphoma with a history of secondary CNS involvement
    • Histologic transformation of indolent lymphoma to large B-cell lymphoma, including marginal zone lymphoma, follicular lymphoma, chronic lymphocytic leukemia (CLL), small lymphocytic lymphoma (SLL), lymphoplasmacytic leukemia, or Waldenstrom macroglobulinemia
    • High risk international prognostic index (IPI) score 4 or 5, at diagnosis or prior to CAR T-cell leukapheresis

  • Patients undergoing allogeneic hematopoietic cell transplantation (alloHCT) for large B-cell lymphoma

• Eastern Cooperative Oncology Group (ECOG) 0-2

• Requirements for post-ASCT and post-alloHCT participants:

  • Disease status of partial response (PR) or complete response (CR) prior to transplantation
  • Receive reduced-intensity conditioning regimen
  • Enrollment no later than day +90

• Requirements for post-CAR T-cell therapy participants:

  • Disease status of PR or CR after post-CAR T-cell therapy positron emission tomography (PET)-computed tomography (CT) at 1-3 months
  • Enrollment no later than day +104

• Ability to give full informed consent

• Female subjects who are sexually active and can bear children must agree to use highly effective forms of contraception while on the study and for 2 days after the last dose of acalabrutinib

• Willing and able to participate in all required evaluations and procedures in this study protocol, including swallowing capsules and tablets without difficulty

• Absolute neutrophil count (ANC) > 500/uL (microliters)

• Platelets > 50,000/uL independent of transfusions

• Hemoglobin > 8 g/dL independent of transfusions

• Serum aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 3 x upper limit of normal (ULN)

• Total bilirubin =< 1.5 x ULN, unless directly attributable to Gilbert's syndrome

• Creatinine clearance >= 60 mL/min based on Cockcroft-Gault glomerular filtration rate (GFR) and serum creatinine (Cr) =< 1.8 mg/dL

Exclusion Criteria:

• Cord blood as donor source in alloHCT
• New York Heart Association Class III or IV
• Left ventricular ejection fraction < 50%
• Estimated glomerular filtration rate < 30 mL/min
• Concurrent long-term use of posaconazole or other strong CYP3A4 inhibitors and unable to replace with equivalent medication
• Acute or chronic graft-versus-host disease (GvHD) >= stage 3 at time of enrollment
• Received packed red blood cells (pRBC) transfusion within the past 2 weeks
• Received platelet transfusion within the past 1 week
• Active invasive fungal infection
• Active bacterial or viral infection until resolution of the infection
• History of or ongoing confirmed progressive multifocal leukoencephalopathy (PML)
• Received any investigational drug within 30 days or 5 half-lives (whichever is shorter) before first dose of study drug
• Major surgical procedure within 30 days before the first dose of study drug. Note: If a subject had major surgery, they must have recovered adequately from any toxicity and/or complications from the intervention before the first dose of study drug
• Refractory nausea and vomiting, inability to swallow the formulated product, or malabsorption syndrome; chronic gastrointestinal disease, gastric restrictions, or bariatric surgery such as gastric bypass; partial or complete bowel obstruction, or previous significant bowel resection that would preclude adequate absorption, distribution, metabolism, or excretion of study treatment
• Received a live virus vaccination within 28 days of first dose of study drug
• Known history of infection with human immunodeficiency virus (HIV)
• History of bleeding diathesis (e.g., hemophilia, von Willebrand disease)
• Requires or receiving anticoagulation with warfarin or equivalent vitamin K antagonists
• Requires treatment with a strong cytochrome P450 3A (CYP3A) inhibitor or inducer. The use of strong CYP3A inhibitors within 1 week or strong CYP3A inducers within 3 weeks of the first dose of study drug is prohibited
• Breastfeeding or pregnant
• Concurrent participation in another therapeutic clinical trial