CD123-Directed T-Cell Therapy for Acute Myelogenous Leukemia (CATCHAML)

The CD123-CAR T-cell therapy is a new treatment that is being investigated for treatment of AML/myelodysplastic syndrome (MDS), T- or B- acute lymphoblastic leukemia (ALL) or blastic plasmacytoid dendritic cell neoplasia (BPDCN). The purpose of this study is to find the maximum (highest) dose of CD123-CAR T cells that is safe to give to these patients. This would include studying the side effects of the chemotherapy, as well as the CD123-CAR T-cell product on the recipient's body, disease and overall survival. Primary Objective: * To determine the safety of one intravenous infusion of escalating doses of autologous, CD123-CAR T cells in patients (≤21 years) with recurrent/refractory CD123+ disease (AML/MDS, B-ALL, T-ALL or BPDCN) after lymphodepleting chemotherapy. * To determine the safety of an intravenous infusion of escalating doses of donor derived, CD123-CAR T cells in patients (≤21 years) with recurrent/refractory CD123+ disease (AML/MDS, B-ALL, T-ALL, BPDCN or MPAL) after lymphodepleting chemotherapy. Secondary Objectives \- To evaluate the antileukemia activity of CD123-CAR T cells. Exploratory Objectives * To assess the immunophenotype, clonal structure and endogenous repertoire of CD123-CAR T cells and unmodified T cells * To characterize the cytokine profile in the peripheral blood and CSF after treatment with CD123-CAR T cells * To characterize tumor cells post CD123-CAR T-cell therapy * To compare in vivo properties of donor-derived versus autologous CD123- CAR T cells