• 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 in pregnancy or impregnation of their partner must use an acceptable method of contraception§ from enrollment until 4 weeks after completing study treatment.