Prophylactic TCRaB+ and CD19+ Depleted Donor Lymphocyte Infusion After Allogeneic Stem Cell Transplant in High-Risk Patients With Hematologic Malignancies

Inclusion Criteria: * Patients with high-risk myeloid or lymphoid malignancies determined to be eligible to undergo a related, allo-SCT using Disease Risk Index (DRI), including the conditions listed below. 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 percent 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 * Other high risk hematologic malignancies for which allo-SCT is deemed clinically necessary per PI and based on institutional standards * The donor for the allo-SCT will have been identified prior to participant recruitment and must be: * Related AND * Matched OR mismatched OR haploidentical at Human Leukocyte Antigen (HLA) HLA-A, -B, -C, and -DRB1 by molecular methods * Eastern Cooperative Oncology Group (ECOG) performance score of 0-2 * Ability to understand and willingness to sign written informed consent document * Willing to comply with all study procedures and be available for the duration of the study * Individuals in sexual relationships that could result…