Inclusion Criteria:

- Have a consenting related haplo-identical (3/6 or 4/6) 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.