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