Single or Double Donor Umbilical Cord Blood Transplant in Treating Patients With High-Risk Hematologic Malignancies

This study will determine the safety and applicability of experimental forms of umbilical cord blood (UCB) transplantation for patients with high risk hematologic malignancies who might benefit from a hematopoietic stem cell transplant (HSCT) but who do not have a standard donor option (no available HLA-matched related donor (MRD), HLA-matched unrelated donor (MUD)), or single UCB unit with adequate cell number and HLA-match).