Dose-ranging Study of a Single Administration of T-cell Add-back Depleted of Host Alloreactive Cells in Patients Undergoing a Peripheral Blood Stem Cell Transplant From a Related, Haploidentical Donor

Inclusion Criteria:

* Any of the following hematologic malignancies: very high risk leukemia, acute leukemia, chronic myeloid leukemia (CML), lymphoma, multiple myeloma (MM), myelodysplastic syndrome (MDS)
* Incompatibility at two to three loci (HLA-A, B and/or DR) or a single DR locus of the unshared haplotype between the donor and recipient
* Life expectancy of at least 3 months
* Satisfactory performance status (ECOG ≤ 2);

Exclusion Criteria:

* Possibility of performing an allogeneic transplant with an HLA (human leukocyte antigen) matched sibling donor
* Availability of an 6/6 HLA-A, B and DRB1 matched unrelated donor within 2-3 months;
* Pregnancy
* Viral hepatitis (B or C)
* Active serious infectious process
* HIV positivity;
* Systemic dysfunction (cardiac, pulmonary, hepatic and renal) contra-indicating allogeneic stem cell transplantation
* Prior allogeneic transplantation
* Prior autologous transplantation within twelve months of baseline visit
* Any abnormal condition or laboratory result that is considered by the principal investigator capable of altering patient condition or study outcome
* Active central nervous system (CNS) disease at baseline
* Participation in a trial with an investigational agent within 30 days prior to entry in the study
* Malignant cells in circulating peripheral blood (\> 25%)
* Other active malignant disease that would severely limit life expectancy