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 allo-SCT including but not limited to the conditions listed below. These criteria apply at the disease diagnosis or any time prior to the cyto-reductive therapy given before the planned conditioning: * Refractory acute myelogenous (AML) or lymphoid leukemia (ALL) * Relapsed AML or ALL * AML in European LeukemiaNet (ELN) high risk per cytogenetic and mutation * Any patients with minimal residual disease (MRD+) disease by flow cytometry or with active disease (not in complete remission (CR)) prior to allo-SCT * Myelodysplastic syndromes (MDS) with 5% or more blasts at initial diagnosis, or anytime during their treatment prior to allo-SCT. * Myelodysplastic syndrome (MDS) high risk or very high risk per Revised International Prognostic Scoring System (IPSS-R) or Molecular International Prognostic Scoring System (IPSS-M) * Chronic myelogenous leukemia (CML) in chronic phase failed 3 or more treatments, in accelerated or blast phase * High risk primary myelofibrosis (PMF) per Dynamic International Prognostic Scoring System (DIPSS)-plus or Mutation-enhanced International Prognostic Scoring System for Transplant-age Patients (MIPSS70+) * PMF in accelerated or blast 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 must be: * Related AND * Matched OR mismatched OR haploidentical at HLA-A, -B, -C, and -DRB1 by molecular methods * 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 in pregnancy or impregnation of their partner must use an acceptable method of contraception§ from enrollment until 4 weeks after completing study treatment. Exclusion Criteria: • Poor organ function as follows (According to the pre-transplant workups results): * Creatinine ≥ 2.0 mg/dL * SGOT and SGPT ≥ 5 x ULN. Liver biopsy per clinician discretion. * Bilirubin ≥ 3 x ULN (unless Gilbert's syndrome) * DLCO \< 50% corrected for hemoglobin * Left ventricular ejection fraction or shortening fraction \< 40% NOTE: Exceptions to the above organ function exclusion criteria are allowable only with assent of the PI since the risks and benefits must be addressed for patients with potentially incurable hematologic malignancies. Such exceptions will be clearly documented in the subject's research record and will not be considered a deviation. * Patients with uncontrolled intercurrent illness * Patients with psychiatric illness/social situations that would limit compliance with study requirements