Study of Brexucabtagene Autoleucel Plus Dasatinib in Adults With Acute Lymphoblastic Leukemia

Inclusion Criteria: * Relapsed or refractory B-precursor ALL defined as one of the following: * Primary refractory disease (\>=5% blasts or persistent extramedullary disease following induction therapy) * First or later relapse of marrow or extramedullary disease * Persistence of MRD defined as detectable ALL by flow cytometry, PCR, or next-generation sequencing * Relapsed or refractory disease after allogeneic transplant provided individual is at least 100 days from transplant at time of enrollment * Patients with isolated, asymptomatic CNS relapse will be eligible * Age \>=18 years * Eastern cooperative oncology group (ECOG) performance status of 0-2 * Adequate renal, hepatic, pulmonary and cardiac function defined as: * Creatinine clearance (as estimated by Cockcroft Gault) ≥ 60 cc/min * Serum alanine aminotransferase (ALT)/aspartate aminotransferase (AST) ≤ 2.5 x upper limit of normal (ULN) * Total bilirubin ≤ 1.5 mg/dl, except in individuals with Gilbert's syndrome. * Cardiac ejection fraction ≥ 50%, no evidence of clinically significant pericardial effusion, and no clinically significant arrhythmias * Baseline oxygen saturation \> 92% on room air * QTc ≤ 500ms * In individuals previously treated with blinatumomab, CD19 tumor expression in bone marrow or peripheral blood by flow cytometry or extramedullary site by IHC or flow cytometry * Negative serum or urine beta-HCG test in females of childbearing potential within 3 weeks of enrollment * Subjects of childbearing or child fathering potential must be willing to practice birth control from the time of enrollment on this study Page 10 of 83 Version 1.0 dated 27-April-2023 and for six (6) months after receiving the preparative conditioning regimen. * Must be able to give informed consent. Legal authorized representative (LAR) is permitted if subject is cognitively able to provide verbal assent. Exclusion Criteria: * History of dasatinib intolerance * Known sensitivity or allergy to aminoglycosides or any agents/reagents used in this study * Blast count \> 75% in the bone marrow. * History of malignancy other than non-melanoma skin cancer or carcinoma in situ (e.g. cervix, bladder, breast) unless disease free for at least 2 years * Presence of CNS-3 disease with neurological changes * History or presence of any CNS disorder such as a seizure disorder, cerebrovascular ischemia/hemorrhage with clinical signs or symptoms * History of concomitant genetic syndrome such as Fanconi anemia, Kostmann syndrome, Shwachman-Diamond or any known bone marrow failure syndrome * History of myocardial infarction, cardiac angioplasty or stenting, unstable angina, or other clinically significant cardiac disease within 12 months of enrollment * Primary immunodeficiency * Known infection with HIV, hepatitis B (HBsAg positive) or untreated hepatitis C virus * Presence of fungal, bacterial, viral, or other infection that is uncontrolled or requiring IV antimicrobials for management. * Salvage chemotherapy including TKIs for Ph+ ALL within 1 week prior to enrollment * Pregnant or breast feeding * Patients with known autoimmune disease requiring the use of systemic immunosuppressive therapy within the last year * Corticosteroid therapy within 7 days prior to enrollment * Acute or chronic GVHD requiring systemic treatment within 4 weeks prior to enrollment * Live vaccine ≤ 4 weeks prior to enrollment * Any medical condition that in the judgement of the investigator is likely to interfere with assessment of safety or efficacy of study treatment