Composition and mechanism of action of a new “designed” graft. It contains a megadose of CD34+ cells that are depleted of TCRαβ+/CD19+ cells plus adoptive immunotherapy with FoxP3Tregs and Tcons in an established ratio of 2:1. Besides the GVL effect, Tcons, NK cells, and TCRγδ+ T cells hasten immune reconstitution.