Efficacy and Safety of a Donor Lymphocyte Preparation Depleted of Functional Host Alloreactive T-cells (ATIR) in Patients Undergoing a Peripheral Blood Stem Cell Transplant From a Related, Haploidentical Donor

Inclusion Criteria: One of the following hematological malignancies: * Acute Myeloid Leukemia (AML) * Acute Lymphoblastic Leukemia (ALL) * Myelodysplastic Syndrome (MDS) * Ph-positive chronic myeloid leukemia (CML) * Non-Hodgkin Lymphoma (NHL) * Myelodysplastic Syndrome (MDS) * Chronic Myeloid Leukemia (CML) * Multiple Myeloma (MM) * Chronic Lymphocytic Leukemia (CLL) * Myeloproliferative Syndrome (MPS) Exclusion Criteria: * AML in 1st complete remission with good risk karyotypes * MM featuring concurrent extramedullar disease or being non-responsive to prior therapy * CML in blast crisis * CLL concurrently transformed into high-grade lymphoma and failing to demonstrate at least partial remission * NHL with concurrent bulky disease (≥ 5 cm) * Diffusing Capacity for Carbon Monoxide (DLCO) \< 40% predicted * Left ventricular ejection fraction \< 40% * AST/SGOT \> 2.5 x ULN * Bilirubin \> 1.5 x ULN * Creatinine \> 1.5 x ULN * HIV positive * Positive pregnancy test for women of childbearing age * Prior haploidentical peripheral blood stem cell or cord blood transplantation * Less than 2 years from a prior allogeneic stem cell transplantation * Estimated probability of surviving less than three months * Major anticipated illness or organ failure incompatible with survival from transplant * Severe psychiatric illness or mental deficiency sufficiently severe as to make compliance with the transplant treatment unlikely and informed consent impossible * Known allergy to any of the components of ATIR * Any other condition which, in the opinion of the investigator, makes the patient ineligible for the study Donor Inclusion Criteria: * Haploidentical family donor with 2 to 3 mismatches at the HLA-A, -B and/or DR loci of the unshared haplotype. * Male or female, age ≥ 16, ≤ 75 years. * Donors must be fit to receive G-CSF and undergo apheresis (normal blood count, normotensive and no history of stroke). * Donor must have Eastern Cooperative Oncology Group (ECOG) performance status of 2 or less. * Donor must provide written informed consent. Donor Exclusion Criteria: * Medically uncontrolled coronary heart disease. * Myocardial infarction within the last 3 months. * History of uncontrolled seizures. * History of malignancy (except basal cell or squamous carcinoma of the skin, positive PAP smear and subsequent negative follow up). * Positive test result for any of the mandatory viral tests in the applicable region, except for a positive cytomegalovirus (CMV) result, which does not lead to exclusion. * Presence of a transmissible disease (such as HIV positive), a major illness, a suspected systemic dysfunction and/or an active inflammatory or autoimmune disorder. * Female donors who are pregnant or nursing.