Inclusion Criteria:

          -  First 2 subjects: male and female subjects age ≥18 and < 27 years (as of 2/16/18 the
             first 2 subjects were enrolled and treated); subsequent subjects <31 years.

          -  Diagnosis of CD19+22+ leukemia

          -  Disease status:

               -  If post allogeneic HCT: Confirmed CD19+CD22+ leukemia recurrence defined as at
                  least 0.01% disease following allogeneic HCT

               -  If relapse/refractory status with no prior history of allogeneic HCT, one of the
                  following:

               -  Second or greater marrow relapse, with or without extramedullary disease

               -  First marrow relapse at end of first month or re-induction with marrow having at
                  least 0.01 % blasts by morphology and/or MPF

               -  Primary refractory as defined as greater than 5% blasts by multi-parameter flow
                  after at least 2 separate induction regimens.

               -  Subject has indication for HCT but has been deemed ineligible, inclusive of
                  persistent MRD prior to HCT

          -  Asymptomatic from CNS involvement, if present, and in the opinion of the Principal
             Investigator with a reasonable expectation that disease burden can be controlled in
             the interval between enrollment and T-cell infusion. Subjects with significant
             neurologic deterioration will not be eligible for T-cell infusion until stabilized.

          -  Free from active GVHD and off immunosuppressive GVHD therapy for 4 weeks prior to
             enrollment

          -  Lansky or Karnofsky performance score of at least 50

          -  Life expectancy of at least 8 weeks

          -  Recovered from acute toxic effects of all prior chemotherapy, immunotherapy, and
             radiotherapy

          -  At least 7 days post last chemotherapy administration (excluding intrathecal
             maintenance chemotherapy)

          -  At least 7 das post last systemic corticosteroids administration (unless physiologic
             replacement dosing)

          -  No prior genetically modified cell therapy that is still detectable or virotherapy

          -  Adequate organ function

          -  Adequate laboratory values

          -  Willing to participate in long-term follow-up for up to 15 years, if enrolled in the
             study and receive T cell infusion

          -  Patients of childbearing/fathering potential must agree to use highly effective
             contraception from the time of initial T cell infusion through 12 months following the
             last T cell infusion

        Exclusion Criteria:

          -  Presence of active clinically significant CNS dysfunction

          -  Pregnant or breast-feeding

          -  Unable to tolerate apheresis procedure

          -  Presence of active malignancy other than CD19+CD22+ leukemia

          -  Presence of active severe infection

          -  Presence of any concurrent medical condition that, in the opinion of the Principal
             Investigator, would prevent the patient from undergoing protocol-specified therapy