Inclusion Criteria:

• Patients with a diagnosis of hematological malignancy undergoing a related donor haploidentical HCT.*
• Patients aged ≥18 are eligible.
• Bilirubin ≤ 2 x the upper limit of normal (ULN). For patients with Gilbert's syndrome or suspected mild veno-occlusive disease, bilirubin ≤ 3 x ULN is permitted.
• Adequate renal function as defined by a serum creatinine clearance of > 30 mL/min calculated by Cockcroft-Gault equation.
• Left ventricular ejection fraction ≥40%. No uncontrolled arrhythmias or New York Heart Association class III-IV heart failure.
• Forced expiratory volume (FEV1) or diffusion capacity for carbon monoxide (DLCO) corrected for hemoglobin ≥ 50% of predicted.
• Karnofsky performance status > 60.
• Graft source of peripheral blood (the infused cluster of differentiation 34 (CD34)+ cell dose will be capped at 5 x 10^6 CD34+ cells/kg recipients actual body weight) or bone marrow (the ideal infused total nucleated cell dose (TNC) will be targeted at 4 x 108/kg recipient actual body weight).
• A negative pregnancy test will be required for all women of child bearing potential. Females of child bearing potential should agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent form through 90 days after the last dose of study drug and must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, or agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence [e.g., calendar, ovulation, symptothermal, postovulation methods] and withdrawal are not acceptable methods of contraception.). Breast-feeding is not permitted.
• Male patients, even if surgically sterilized (i.e., status post-vasectomy), must agree to one of the following: practice effective barrier contraception during the entire study treatment period and through 90 days after the last dose of study drug, or must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, or agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods] and withdrawal are not acceptable methods of contraception.)
• No evidence of uncontrolled bacterial, viral or fungal infections at the time of enrollment.
• Transplant recipient able to give informed consent. * Patients must be human leukocyte antigen (HLA) typed at high resolution using DNA based typing at the following HLA loci: HLA-A, -B, -C and DRB1 and have available: A related haploidentical bone marrow donor with two, three or four HLA-mismatches. A unidirectional mismatch in either the graft-versus-host or host-versus-graft direction is considered a mismatch. The donor and recipient must be HLA identical for at least one antigen (using high-resolution DNA-based typing) at the following genetic loci: HLA-A, HLA-B, HLA-C, and HLA-DRB1. Fulfillment of this criterion shall be considered sufficient evidence that the donor and recipient share one HLA haplotype, and typing of additional family members is not required.

Exclusion Criteria:

• Patient must not have a healthy, eligible and readily available HLA-identical sibling donor or a volunteer adult unrelated donor (matched at allele-level at HLA-A, -B, -C and -DRB1).
• No serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol.\
• Presence of active disease in acute myeloid leukemia (AML)/myelodysplastic syndrome (MDS): patients with active disease defined as >5% blasts in bone marrow and/or circulating leukemic blasts in peripheral blood, patients with known active central nervous disease involvement with leukemia/lymphoma or lymphoma patients with progressive disease on clinical and/or radiographic assessment are not eligible for this study.