ARM I: Patients receive lymphodepleting regimen per treating physician's discretion 3-10 days before the T-cell infusion. Patients receive CD19CAR-CD28-CD3zeta-EGFRt-expressing Tcm-enriched T cells IV over 15 minutes on day 0. Patients who have evidence of disease, whose tumor(s) continue to express the appropriate antigen target may receive an optional second infusion of CD19CAR-CD28-CD3zeta-EGFRt-expressing Tcm-enriched T cells after 28 days.