Phase I/Ib Clinical Trial of Autologous CD22 Chimeric Antigen Receptor (CAR) T Cells Following Commercial CD19 CAR T Cells in Children and Young Adults With Recurrent or Refractory B Cell Malignancies

Inclusion Criteria: 1. Diagnosis of histologically confirmed relapsed/refractory (R/R) B cell acute lymphoblastic leukemia (ALL) 2. Must be eligible to receive commercial KYMRIAH® (tisagenlecleucel) according to FDA approved package insert (refractory disease or in second or later relapse) 3. CD19 and CD22 expression must be demonstrated on malignant cells by immunohistochemistry or flow cytometry. CD19 and CD22 expression at any level of expression will be acceptable, as that is the standard for commercial KYMRIAH® (tisagenlecleucel) and the optimal level of CD22 expression is not well defined. 4. Age: ≥ 1 year of age and ≤ 25 years and 364 days of age at time of enrollment. 5. Performance Status: Participants \> 16 years of age: Karnofsky ≥ 50%; Participants ≤ 16 years of age: Lansky scale ≥ 50%. 6. Normal Organ and Marrow Function * Absolute Neutrophil Count (ANC) ≥ 750/uL\* * Platelet count ≥ 50,000/uL\* * Absolute Lymphocyte Count ALC \> 150/uL\* * Adequate renal, hepatic, pulmonary and cardiac function defined as: * Baseline oxygen saturation \> 92% on room air * Creatinine within ULN for age or Creatinine clearance (as estimated by Cockcroft Gault Equation) ≥ 60 mL/min * Total bilirubin ≤ 1.5 mg/dl, except in Participants with Gilbert's syndrome. \[Elevations related to leukemia involvement of the liver will not disqualify a subject\] * Alanine Transaminase (ALT) or Aspartate Aminotransferase (AST) ≤ 10 x ULN (except in Participants with liver involvement by leukemia) * Cardiac ejection fraction ≥ 40%, no evidence of pericardial effusion as determined by an Echocardiogram. * if these cytopenias are not judged by the investigator to be due to underlying disease (i.e. potentially reversible with anti-neoplastic therapy); A subject will not be excluded because of pancytopenia ≥ Grade 3 if it is due to disease, based on the results of bone marrow studies. 7. Participants with Central Nervous System (CNS) involvement or a history of CNS involvement are eligible only in the absence of neurologic symptoms that may mask or interfere with neurological assessment of toxicity 8. Participants who have undergone autologous SCT with disease progression or relapse following SCT are eligible. Participants with history of allogeneic SCT must be at least 100 days from SCT, have no evidence of Graft versus Host Disease (GvHD), and no longer taking immunosuppressive agents for at least 30 days prior to enrollment. 9. Females of child bearing potential and males of child fathering potential must be willing to practice birth control during and for 4 months post chemotherapy or for as long as Chimeric Antigen Receptor (CAR) T cells are detectable in peripheral blood. 10. Females of child bearing potential must have negative pregnancy test. 11. Must meet wash out period since prior therapies according to commercial KYMRIAH® (tisagenlecleucel) SOPs. 12. Must have recovered from acute side effects from prior therapy to meet eligibility. 13. If had prior CAR therapy, will be eligible if at least 30 days has elapsed prior to apheresis. 14. Ability to give informed consent. All Participants ≥ 18 years of age must be able to give informed consent. For participants \<18 years old their legal authorized representative (LAR) (i.e. parent or guardian) must give informed consent. Pediatric participants will be included in age appropriate discussion and assent per institutional SOPs will be obtained for those \> 7 years of age, when appropriate. If a minor becomes of age during participation of this study, he/she will be asked to reconsent as an adult. * A subject will not be excluded because of pancytopenia ≥ Grade 3 if it is felt by the investigator to be due to underlying disease. Exclusion Criteria: 1. May not have Human Immunodeficiency Virus (HIV)/Hepatitis B (HBV) or Hepatitis C (HCV infection) or uncontrolled, symptomatic, intercurrent illness. 2. May not have hyperleukocytosis (≥ 50,000 blasts/μL) or rapidly progressive disease that in the estimation of the investigator and sponsor would compromise ability to complete study therapy. 3. May not have severe, immediate hypersensitivity reaction attributed to compounds of similar chemical or biologic composition to any agents used in study. 4. May not have active CNS disorder, or history of MI, cardiac angioplasty or stenting, unstable angina or other clinically significant cardiac disease with 12 months of enrollment. 5. May not have primary immunodeficiency or history of autoimmune disease (e.g. Crohns, rheumatoid arthritis, systemic lupus) requiring systemic immunosuppression/systemic disease modifying agents within the last 2 years.