Study of Haplo-HSCT + Rivogenlecleucel vs Haplo-HSCT + Post Transplant Cyclophosphamide in Patients With AML or MDS

In the Phase 2 portion, participants will undergo αβ T cell and CD19+ B cell depleted haploidentical HSCT followed by an infusion of a fixed dose of rivogenlecleucel (BPX-501 T cells) per kg. These participants will be evaluated for prespecified dose limiting toxicities (DLTs) for a 100-day dose limiting toxicity window. Following completion of the Phase 2 portion, participants will be enrolled and randomized to one of two treatment arms in the Phase 3 portion. * Arm A:αβ T-cell and CD19+ B-cell-depleted haplo-HSCT plus treatment with rivogenlecleucel * Arm B: haplo-HSCT plus post transplant cyclophosphamide Pediatric patients ages 12-17 will also be included in US only.