This study is a Phase 1, Non-randomized, Open-label/Phase 2 Randomized, Blinded Study of ProTmune (ex vivo programmed mobilized peripheral blood cells) Versus Non-programmed mobilized peripheral blood cells for Allogeneic Hematopoietic Cell Transplantation (HCT) in Adult Subjects Aged 18 to 70 years with Hematologic Malignancies. A maximum of 70 total eligible subjects will be enrolled and treated in the trial at approximately 15-20 centers in the US and EU.