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.

Primary Objectives: To assess the Efficacy of Brexucabtagene autoleucel \[anti-CD19 autologous derived chimeric antigen receptor T-cell (CAR-T)\] in terms of EFS in patients with R/R and high-risk newly diagnosed B-cell acute lymphoblastic leukemia (B-cell ALL) post cytoreduction with mini-hyper-CVD-inotuzumab-blinatumomab/Hyper-CVAD-inotuzumab-blinatumomab The EFS will be estimated in terms of median EFS and 9-month EFS for the R/R cohort and 18-month EFS for the frontline cohort. Secondary Objectives: 1. 12 and 24-months overall survival (OS): 12 months for the R/R cohort and 24 months for the frontline cohort 2. Duration of persistent MRD negativity by flow cytometry and NGS at 9 and 18 months: 9 months for the R/R cohort and 18 months for the frontline cohort 3. Best Ooverall response rates \[complete remission (CR) and CR with incomplete count recovery (CRi)\] 4. Achievement of MRD negativity amongst patients in CR and not MRD negative before Brexucabtagene autoleucel infusion 5. Safety Exploratory Objectives: 1. CAR-T-cell expansion ((Days 1, 4, 8, 11, 14, 21, 28, monthly up to 3 months and then every 3 months up to 24 months post infusion) 2. B-cell aplasia (Days 0, 7, 14, 28, monthly up to 3 months and then every 3 months up to 24 months post infusion) 3. Measurable residual disease (MRD) negativity by next-generation sequencing (NGS) (at 1 in 105-6 sensitivity) (PB on D14 and PB/BM: Day 28, and then Q3 months up to 24 months post infusion) 4. Cytokine panel (Days 0, 1, 2, 4, 7, 10, 14, 28) 5. Additional correlatives samples to address tumor samples and immune system factors will be collected at baseline, D28 and Q3 months. These include samples for bulk RNA sequencing of the tumor and germline and single cell RNA sequencing of CAR T-cells as also for assessing the methylation signatures of the CAR T-cells.

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