Adoptive Immunotherapy in Relapsed Hematological Malignancy: Early GVHD Prophylaxis

Inclusion Criteria * Any of the following high risk or recurrent hematological malignancies: * Hodgkin lymphoma (HL) * Non-Hodgkin lymphoma (NHL) * Chronic lymphocytic leukemia (CLL) * Multiple myeloma (MM) * Acute myelogenous leukemia (AML) * Acute lymphocytic leukemia (ALL) * Chronic myelogenous leukemia (CML) * Myelodysplastic syndrome (MDS) \*Note: Determination that the malignancy is high risk will be made by the investigator. * Investigator determination that the patient is an appropriate candidate for reduced intensity allogeneic SCT with the standard Massey Cancer Center-Virginia Commonwealth Health System Bone Marrow Transplant Massey Cancer Center Virginia Commonwealth University Health System Bone Marrow Transplant (MCC-VCUHS BMT) Program regimen employed in this trial * Patients with or without previous myeloablative autologous transplant * HLA-matched stem cell donor, either related (6/6 or 5/6 loci matched) or unrelated (8/8 or 7/8 loci matched) \*Note: Unrelated donors must be matched at HLA-A, -B, -C, and -DRB1 loci. However, a single locus mismatch will be acceptable in the event a more closely matched donor is not available. * Age ≥ 40 to \< 75 years; patients 18 to 39 years of age will be eligible only if the investigator has determined that the patient has comorbidity(ies) precluding conventional allogeneic transplantation with full intensity myeloablative conditioning * Karnofsky Performance Status of 70-100% * Negative serology for HIV * Women who…