CD19/CD22 Bicistronic Chimeric Antigen Receptor (CAR) T Cells in Children and Young Adults With Recurrent or Refractory CD19/CD22-expressing B Cell Malignancies

Eligibility Criteria

• * Diagnosis
• * Participant must:
• * Have pathology confirmed B cell ALL (not isolated to the testis or CNS), CML with ALL transformation, or high-grade lymphoma (e.g., Burkitt s lymphoma, B-lymphoblastic lymphoma, diffuse large B-cell lymphoma, inclusive of low-grade lymphoma that has transformed to high grade disease); and
• * Have relapsed or been refractory after at least one standard chemotherapy regimen and at least one salvage treatment. Participants with Philadelphia chromosome + ALL must have failed prior tyrosine kinase inhibitor; and
• * Be ineligible for allogeneic stem cell transplant (SCT), have refused SCT, or have recurred after SCT; and
• * Have no evidence of graft-versus- host disease (GVHD) and have been without immunosuppressive agents for at least 30 days prior to apheresis, if undergone prior allogeneic SCT; and
• * Be unable to access (in a timely manner), ineligible for, or have relapsed/failed after or not responded to a commercially available CD19 CAR T-cell construct; and
• * Have evidence of at least minimal residual disease or PET-avid disease (lymphoma) at the time of enrollment.
• * CD22/CD19 expression
• * CD19 must be detected on \>15% of the malignant cells by immunohistochemistry or \> 80% by flow cytometry.
• * CD22 positivity must be confirmed.
• * Age \>= 3 years of age and \<=39 years of age at time of enrollment.
• * Clinical Performance status: Participants \>= 16 years of age: Karnofsky \>= 50%; Participants \< 16 years of age: Lansky scale \>= 50%.
• * Participants must have adequate organ and marrow function as defined below:
• * leukocytes \>= 750/mcL\*
• * platelets \>= 50,000/mcL\*
• * total bilirubin \<=2 X ULN (except in the case of participants with documented Gilbert s disease \> 3x ULN)
• * AST(SGOT)/ALT(SGPT) \<=10 x institutional upper limit of normal
• * creatinine \<= the maximum for age listed in the table below OR
• * measured creatinine clearance \>=60 mL/min/1.73 m\^2 for participants with creatinine levels above the max listed below per age.
• * Age (Years) \<= 5 \|\| Maximum Serum Creatinine (mg/dL) \<= 0.8
• * Age (Years) 6 to \<= 10 \|\| Maximum Serum Creatinine (mg/dL) \<= 1.0
• * Age (Years) \>10 \|\| Maximum Serum Creatinine (mg/dL) \<= 1.2
• * a participant will not be excluded because of pancytopenia \>= Grade 3 if it is due to underlying bone marrow involvement by leukemia
• * Central nervous system (CNS) Status
• * Participants with leukemia with CNS 1 and 2 disease are eligible in the absence of exclusion criteria
• * Participants of child-bearing or child-fathering potential must be willing to practice effective birth control from the time of enrollment until 12 months following completion of study treatment for women and for 4 months following completion of study treatment for men.
• * Participants who are breastfeeding or plan to breastfeed must agree to discontinue/postpone breastfeeding while on study therapy and until 1 month after the administration of CAR.
• * Cardiac function: Left ventricular ejection fraction \>= 45% or fractional shortening \>=28%
• * Pulmonary Function
• * Baseline oxygen saturation \>92% on room air at rest
• * Ability of participant or Legally Authorized Representative (LAR) to understand and the willingness to sign a written informed consent document.
• * Ability and willingness of participant or Legally Authorized Representative (LAR) to co- enroll on 15-C-0028: Follow-up Evaluation for Gene-Therapy Related Delayed Adverse Events after Participation in Pediatric Oncology Branch Clinical Trials.
• * Participants with CNS3 disease, neurologic signs of CNS disease, radiologically detected active CNS lymphoma
• * Hyperleukocytosis (\>= 50,000 blasts/microL)
• * Positive serum or urine beta-HCG pregnancy test performed at screening.
• * Participants will be excluded based on prior therapy if they fail to meet following washout criteria:
• * Therapy: Systemic Chemotherapy, anti-neoplastic agents, antibody- based therapies
• * Washout\*: \>=2 weeks
• * Exceptions: 6 weeks for clofarabine or nitrosoureas; No washout for prior intrathecal chemotherapy, steroid therapy, hydroxyurea (no dose increases within prior 2 weeks) or ALL maintenance-type chemotherapy (vincristine, 6-mercaptopurine, oral methotrexate, or a tyrosine kinase inhibitor for participants with Ph+ ALL) provided there is recovery from any acute toxic effects
• * Therapy: Radiation
• * Washout\*: \>=3 weeks
• * Exceptions: No time restriction with radiation therapy if the volume of bone marrow treated is less than 10% and the participant has measurable/evaluable disease outside the radiation window
• * Therapy: Allogeneic Stem Cell Transplant
• * Washout\*: \>= 100 days since SCT; \>= 30 days since completion of immunosuppression; \>= 6 weeks since donor lymphocyte infusion (DLI)
• * Exceptions: Cannot have evidence of active graft-versus-host disease (GVHD)
• * Therapy: CAR T-Cell Therapy or other Adoptive Cell Therapy
• * Washout\*: \> 30 days post infusion
• * Exceptions: For patients previously treated with CAR T-cells without interim HSCT (cohorts B1 and D1) cannot have circulating CAR T cells (or genetically modified cells) \>5% by flow cytometry in peripheral blood
• * Washout: Time between therapy and apheresis
• * Positive HIV antibodies consistent with active HIV.
• * Positive hepatitis C antibodies or positive Hepatitis B surface antigen (HbsAG) indicative of current/active HCV/HBV.
• * Active second malignancy other than in situ carcinoma of the cervix, unless the tumor was treated with curative intent at least two years previously and participant is in remission.
• * History of severe, immediate hypersensitivity reaction attributed to compounds of similar chemical or biologic composition to any agents used in study or in the manufacturing of the cells.
• * Uncontrolled, symptomatic, intercurrent illness or social situations that would limit compliance with study requirements or in the opinion of the PI would pose an unacceptable risk to the participant.