• ARM A: CD19+/- CD22+ B-ALL with relapsed or refractory disease not responding to conventional chemotherapy and with no other curative therapy available. Treatment with previous CART CD19 therapy is permitted, but is not mandatory, OR:

• ARM B: T-ALL with relapsed or refractory disease not responding to conventional chemotherapy and with no other curative therapy available.

• Patients diagnosed with ALL must be suitable for allogeneic HSCT and willing to proceed to transplant if the CART treatment induces complete remission and the investigator believes it is the best option.

• For ARM B there must be a suitable haploidentical donor (following local standard operating procedures).

• Lansky (age \<16 years) or Karnofsky (age ≥16 years) score of 50 or greater.

• Life expectancy greater than 12 weeks.

• Absolute neutrophil count (ANC) ≥ 500/μL unless, in the opinion of the investigator, cytopenia is due to underlying leukemia and is potentially reversible with leukemia therapy.

• Platelet count ≥ 50,000/μL unless, in the opinion of the investigator, cytopenia is due to underlying leukemia and is potentially reversible with leukemia therapy.

• Absolute lymphocyte count ≥ 100/μL.

• Adequate renal, hepatic, pulmonary, and cardiac function.

• Adequate venous access and absence of contraindications for lymphoapheresis

• Patients with a seizure disorder may be enrolled if well controlled with anticonvulsants.

• Patients or patients' legal representative, parent(s), or guardian able to provide written informed consent.