Phase Ib/II Study Assessing the Clinical Activity and Safety of Brexucabtagene Autoleucel as a Consolidation in Patients With Relapsed/Refractory (R/R) and Newly Diagnosed B-cell Acute Lymphocytic Leukemia (ALL) Post Cytoreduction With Mini-HCVD-inotuzumab-blinatumomab/HCVAD-inotuzumab-blinatumomab

To learn about the safety of giving the drug brexucabtagene autoleucel to participants with relapsed/refractory B-cell ALL after treatment with inotuzumab ozogamicin, blinatumomab, and either hyper-CVAD or mini-hyper-CVD. Also, to learn if giving brexucabtagene autoleucel to patients with relapsed/refractory or high-risk, newly diagnosed B-cell ALL after treatment with inotuzumab ozogamicin, blinatumomab, and either hyper-CVAD or mini-hyper-CVD can help to control the disease.

Inclusion Criteria: * Participants of age ≥18 years with documented relapsed or refractory B-cell ALL * In the newly diagnosed cohort: Participants of age ≥18 years with high-risk newly diagnosed B-cell ALL defined as: 1. KMT2A rearranged ALL 2. Complex cytogenetics as per NCCN 2022 3. Low-hypodiploidy/tetraploidy 4. Philadelphia-like ALL (based on CRLF2 overexpression or recurrent Ph-like genetic fusions) * Performance status of 0, 1, or 2 * Adequate organ function with creatinine less than or equal to 1.6 mg/dl, bilirubin less than or equal to 3.5 mg and ALT and AST less than or equal to 5 times institutional upper limit of normal * Participants should be CD19 expression positive (\>50%) before enrollment * Participants with chronic viral infections like Hepatitis B-virus, Hepatitis C virus or Human Immunodeficiency virus I/II will be eligible if they are on therapy and infections are under control. Exclusion Criteria * Philadelphia positive B-cell ALL * Pregnant or lactating; women of child-bearing potential (WOCBP) must have negative pregnancy test. WOCBP defined as not post-menopausal for 12 months or no previous surgical sterilization * Prior exposure to brexu-cel or other anti-CD-19 CAR T cell therapy * Active and uncontrolled disease/infection as judged by the treating physician * Unable or unwilling to sign the consent form * No other investigational therapy within the past 14 days