 Since, in this study, the donor lymphoid and stem cell portions of the graft are collected and administered at different time points during the conditioning regimen, this approach to haploidentical HSCT is referred to as a 2 Step regimen. The approach does not involve ex vivo T cell depletion, but uses cyclophosphamide to tolerize donor lymphocytes within the framework of a myeloablative conditioning regimen. Preliminary experience with this approach in adult patients at Thomas Jefferson University for myeloablative haploidentical HSCT dates back to 2005 with the first trial using myeloablative conditioning formally launched in 2006. That initial trial met its accrual goals and the current trial is one of the successor trials derived from that experience. 