CD19-CD22-Bispecific Chimeric Antigen Receptor (CAR) T Cell Therapy for Pediatric Patients With Acute Lymphoblastic Leukemia (1922CAR)

Collection and Manufacturing Eligibility Inclusion Criteria: * Age \<21 years old * Relapsed/refractory CD19- and/or CD22-positive acute leukemia defined as: \*CD19 and/or CD22-positivity confirmed within 2 months and after receipt of any CD19 or CD22-directed therapy * Second or greater relapse * Any relapse after allogeneic HCT * Refractory disease (primary or in relapse) despite therapy designed to induce remission * Estimated life expectancy of \> 12 weeks * Karnofsky or Lansky (age-dependent) performance score ≥50 (Appendix A) * For females of childbearing age: * Not lactating with intent to breastfeed * Not pregnant with negative serum or urine pregnancy test within 7 days prior to enrollment Exclusion Criteria: * Known primary immunodeficiency * Known HIV positivity * Known contraindication to receiving protocol defined lymphodepleting * chemotherapy regimen * History of hypersensitivity reaction to murine protein-containing products Treatment Eligibility Inclusion Criteria: * Age \< 21 years old * Detectable disease in the bone marrow * Estimated life expectancy of \> 8 weeks * Karnofsky or Lansky (age-dependent) performance score \> 50 (Appendix A) * Adequate cardiac function defined as left ventricular ejection fraction \>40%, or shortening fraction \> 25% * EKG without evidence of clinically significant arrhythmia * Adequate renal function defined as creatinine clearance or radioisotope GFR \>50 mL/min/1.73m2 (GFR \>40 mL/min/1.73m2 if \<2 years of age) * Adequate pulmonary function defined as forced vital capacity (FVC) \>50% of predicted value; or pulse oximetry \>92% on room air * Total bilirubin \< 3 times the upper limit of normal for age, except in subjects with Gilbert's syndrome * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) \< 5 times the upper limit of normal for age * Has recovered from all NCI CTAE grade III-IV, non-hematologic acute toxicities from prior therapy * Prior to planned CAR T cell infusion, patients with a history of prior allogeneicHCT must be at least 3 months from HCT, have no evidence of acute GVHD, and have not received a donor lymphocyte infusion (DLI) within the 28 daysprior to planned infusion * For females of childbearing age: * Not lactating with intent to breastfeed * Not pregnant with negative serum or urine pregnancy test within 7 days prior to enrollment * If sexually active, agreement to use birth control until 3 months after T cell infusion. Male partners should use a condom. Exclusion Criteria: * Known primary immunodeficiency * Known HIV positivity * Known contraindication to receiving protocol defined lymphodepleting * chemotherapy regimen * History of hypersensitivity reactions to murine protein-containing products * Severe, uncontrolled bacterial, viral or fungal infection * Active CNS-3 disease * Evidence of active, uncontrolled neurologic disease