Phase I Dose Escalation and Preliminary Efficacy Study of Bispecific CD19 and CD22 Chimeric Antigen Receptor Co-Expressing T Cells (CD19x22 CAR T) in Pediatric Patients With Relapsed and/or Refractory B-Cell Acute Lymphoblastic Leukemia (B-ALL)

Inclusion Criteria: 1. Subjects must have a history of B precursor ALL with any of the following conditions: 1. Relapsed two or more times. 2. Relapsed at any time after allogeneic bone marrow transplant (BMT). 3. Relapse or refractory after single antigen targeting CAR T cell therapy. i. 90 days must have elapsed post previous CAR infusion prior to apheresis. d. Refractory to standard therapy as determined by the treating physician. e. Patient and/or parents declining BMT options and would prefer CAR T Therapy. 2. CD19 and/or CD22 present on last relapsed/refractory disease evaluation. 3. Performance score (Lansky or Karnofsky ≥ 50%; or Eastern Cooperative Oncology Group (ECOG) must be ≤2). 4. Meets criteria for potential leukapheresis collection or has leukapheresis product previously collected and stored per recommended guidelines. 5. Males OR non-pregnant, non-lactating females. 6. Aged 3 months to 30 years (inclusive) at time of consent and enrollment. 7. Provision of a signed and dated consent form from parent or guardian (patients \< 18), the patient themselves (\> 18), or legally authorized representative (patient \> 18 who lack decision-making capacity) after standard of care (SOC) screening assessments are performed. 8. Stated willingness to comply with all study procedures and be available for the duration of the study. 9. Willingness to participate in long-term follow-up protocol. Exclusion Criteria: 1. Active, uncontrolled central nervous system (CNS) leukemia that is progressive despite other therapies or leading to CNS symptoms (including but not limited to: seizures, paresis, aphasia, hemorrhage, dementia, psychosis, or movement disorders) as determined by the treating physician at eligibility, prior to lymphodepleting chemotherapy (LD chemo), and pre- CD19x22 CAR T cell infusion. 2. History of allogeneic stem cell transplantation prior to apheresis that meet the following criteria: 1. Less than 100 days post-transplant; 2. Evidence of active Graft-versus-Host Disease (GvHD) requiring systemic therapy; 3. Less than 6 weeks post donor lymphocyte infusion (DLI). 3. Active, uncontrolled, life-threatening infection that at the determination of the treating physician would preclude safe apheresis or tolerance of lymphodepleting chemotherapy, cell infusion, or increased risk of cytokine release syndrome. 4. Evidence of severe organ dysfunction defined by: 1. Baseline oxygen saturation of \< 90% on room air 2. Myocardial dysfunction (based on age standards): Ejection fraction ≤ 40% or shortening fraction ≤ 28%, evidence of physiologically significant pericardial effusion as determined by an echocardiogram (ECHO), and clinically significant electrocardiogram (ECG or EKG) findings 3. Transaminases \> 10x upper limit of normal (ULN) or bilirubin \> 5x the ULN, unless thought to be related to primary disease 4. Estimated Creatinine (Cr) clearance \< 60 mL/min/1.73 m2 (if nuclear medicine GFR or other more specific testing exceeds this level than it can supersede the estimated clearance) 5. Subjects of childbearing or child-fathering potential that are not willing to practice birth control from the time of enrollment on this study and for 12 months after receiving the investigational product 6. Known HIV infection or active Hepatitis B or Hepatitis C infection.