Donor T Cells After Donor Stem Cell Transplant in Treating Patients With Hematologic Malignancies

Inclusion Criteria: * INCLUSION CRITERIA PRIOR TO TRANSPLANT: * The clinical trial will be offered to all high risk (defined 3 below) patients with hematologic malignancies who require stem cell transplants as part of their standard of care using matched related or unrelated donors * Patients with high risk myeloid or lymphoid malignancies at stem cell transplant following American Society for Blood and Marrow Transplantation (ASBMT) criteria, including but not limited to conditions listed; these criteria apply BEFORE cyto-reductive therapy given within 28 days of planned conditioning: * Refractory acute myelogenous or lymphoid leukemia * Relapsed acute myelogenous or lymphoid leukemia * Myelodysplastic syndromes with 5% or more blasts * Chronic myelogenous leukemia in chronic phase 3 or more, blast phase presently, or second accelerated phase * Recurrent or refractory malignant lymphoma or Hodgkin's disease with less than a partial response at transplant * High risk chronic lymphocytic leukemia defined as no response or stable disease to the most recent treatment regimen * DONORS: Matched related or unrelated donor stem cell transplant (SCT) matched at human leukocyte antigen (HLA) A- B, C, and DRB1 by molecular methods; 7 of 8 matched donor acceptable for related donors * T-cell depletion with anti-thymocyte globulin (ATG) (rabbit or horse) or at least 30 mg of alemtuzumab total in the conditioning regimen * Immune suppression; planned post-transplant immune sup…