CD22 CAR T-cells to Extend Remission Following Commercial CD19 CAR T-cells in Children, Adolescents, and Adults With Relapsed/Refractory B-cell Acute Lymphoblastic Leukemia

Background: Acute lymphoblastic leukemia (ALL) is a type of blood cancer. Chimeric antigen receptor (CAR) therapy involves taking immune cells (T cells) from a person and modifying them to better target cancer cells. CAR T-cell therapy that targets a marker called CD19 has been show to can cure ALL in many children and adults. But in about 50% of patients, the ALL comes back within a year. Researchers want to find out if a second treatment with CAR T-cell therapy that targets a different marker, CD22, can keep the cancer away longer. Objective: To see if CD22 CAR T-cell therapy can keep ALL away longer. Eligibility: People aged 3 to 65 years who have no signs of cancer after CD19 CAR T-cell treatment for ALL. Design: Participants will be screened. They will have imaging scans and tests of their heart function. A sample of tissue (biopsy) will be collected from their bone marrow. They will have a fluid sample collected from the area around their spinal cord. Participants will undergo collection of their white blood cells (T cells) during a procedure called leukapheresis. Blood will be taken from their body through a vein. The blood will pass through a machine that separates out the T cells. The remaining blood will be returned to the body through a different vein. The cells will be altered in a lab to create CD22 CAR T-cell therapy. Participants will take drugs over 4 consecutive days to prepare their body for the CAR T-cell therapy; then they will receive their modified T cells through a tube inserted into a vein. Some people may need to stay in the hospital during treatment. Participants will have follow-up visits for 2 years.

* INCLUSION CRITERIA: * Participants must have documentation of pathologic confirmation of a diagnosis of relapsed/refractory B cell acute lymphoblastic leukemia (ALL). * History of CD19 and CD22 expression on malignant cells at diagnosis or relapse. * Age between \>= 3 years and \= 2 months and \= 50% (participants \>= 16 years of age), or Lansky scale \>= 50% (participants \< 16 years of age). Participants who are unable to walk because of paralysis, but who are upright in a wheelchair may be considered eligible. * Must have no ongoing signs of CRS from prior CAR T cell infusion and/or ICANs at screening. * Participants must have adequate organ function as defined below: * Total bilirubin \