Expanded Access to T-cell Depleted Haplo-Identical Stem Cells for Patients Receiving Haplo-Identical and Unrelated Cord Blood Transplants

Inclusion Criteria: * Have a consenting related haplo-identical (3/6, 4/6, or 5/6 if DRB1 mismatch) stem cell donor. * Have one or two available 4, 5, or 6/6 antigen matching unrelated UCB unit(s) that will deliver a total cell dose \>3.0 x 10e7 cells/kg. Patients who do not have a single UCB unit that will deliver the minimum required cell dose, two partially HLA-matched UCB units which together meet the minimum cell dose requirement, can be used for 1 transplant. These units must be HLA-matched minimally at 4 of 6 HLA-A and B (at intermediate resolution by molecular typing) and DRB1 (at high resolution by molecular typing) loci with the patient, and HLA-matched at 3 of 6 HLA- A, B, DRB1 loci with each other (using same resolution of HLA typing as indicated above). There is no limitation on maximum cell dose. * Have a high risk or refractory malignancy, or non-malignant disorder amenable to stem cell transplantation therapy. * Meet eligibility requirements for allogeneic transplant per institutional standard practices. * Have given written informed consent according to FDA guidelines (or consent of parent/legal guardian as applicable). * Be \<65 years of age at the time of study enrollment. Exclusion Criteria: * Have a consenting 8/8 or 10/10 allele matched, consenting, related or unrelated hematopoietic stem cell transplant (HSCT) donor. * Have a life expectancy of less than 3 months. * Have uncontrolled infections at time of cytoreduction.