Patients receive fludarabine phosphate intravenously (IV) over 30 minutes on days -4 to -2 and cyclophosphamide IV over 60 minutes on day -2. Patients then receive CD19/CD22-CAR T cells IV over 10-20 minutes on day 0. Patients that benefited from the first dose of CD19/CD22-CAR T cells, had no unacceptable side effects, and have enough cells left over may receive 2 or 3 additional doses of CD19/CD22-CAR T cells.