Haplo-identical Natural Killer (NK) Cells to Prevent Post-Transplant Relapse in AML and MDS (NK-REALM)

Inclusion Criteria: 1. Age 18 to 65 years. 2. Weight at least 45 kg. 3. Patients with AML must have high risk for disease relapse AND be in complete remission (CR), complete remission with incomplete hematologic recovery (CRi) or morphologic leukemia free state (MLFS). Patients with FLT3 internal tandem duplication (FLT3/ITD) mutation are eligible but must be made aware of alternative treatments available, e.g. tyrosine kinase inhibitor therapy as maintenance following transplantation. * AML patients must be in CR, CRi or a MLFS, as defined by ELN 2017. 4. Patients with high-risk MDS must meet one of the following criteria: * i. De novo MDS with intermediate/high/very high Revised International Prognostic Scoring System (R-IPSS) risk scores with 1. Bone marrow blasts \< 10%, AND 2. Patients may be treatment-naïve, or have received prior treatment with hypomethylating agents or other therapies. * ii. Secondary/therapy-related MDS with bone marrow blasts \< 10%. 5. Hematopoietic Cell Transplantation Comorbidity Index (HCT-CI) of 3 or less. The presence of prior malignancy will not be used to calculated HCT-CI for this trial to allow for the inclusion of patients with secondary or therapy-related AML or MDS. 6. Cardiac function: LVEF ≥ 45%. 7. Pulmonary function: DLCO corrected for hemoglobin ≥ 60% and FEV1 ≥ to 60% the predicted value. 8. Serum creatinine \< 1.5 mg/dL or creatinine clearance by Cockroft-Gault ≥ to 50 ml/min 9. Hepatic ALT/AST \< 5 x the institutional upper limit of normal (ULN) and total bilirubin \< 1.5 mg/dl with conjugated (direct) bilirubin \< 2 x ULN. a. Indirect hyperbilirubinemia due to Gilbert's syndrome is allowed including total bilirubin ≥ to 1.5 mg/dl 10. Karnofsky Performance Score ≥ to 70%. 11. Available first-degree related mismatched bone marrow donor \[biologic parent, siblings (full or half) or children\] as follows: 1. Donor must be at least a full haplotype match (3/6 or 4/6 match only; 5/6 matches are not allowed) for human leukocyte antigen (HLA)-A and -B at intermediate (or higher) resolution, and -DRB1 at high resolution using DNA-based typing, AND 2. Donor must be willing to donate bone marrow, AND 3. Donor should be a candidate for bone marrow harvest, according to institutional standards. 12. Female patients must either: 1. Be of non-childbearing potential, either postmenopausal or surgically sterilized. 2. Or, if of childbearing potential agree to practice two effective methods of contraception or agree to completely abstain for intercourse from the time of signing the informed consent form through receiving immunosuppressive therapy post-transplant. 13. Male patients (even if surgically sterilized), and their female partners of childbearing potential must agree to use a highly effective contraception method. 14. Voluntary written consent obtained prior to the performance of any study-related procedure. Exclusion Criteria: 1. Prior allogeneic transplant. 2. AML beyond CR2. 3. Patients who have a suitable HLA-matched related donor. 4. Donor specific anti-HLA antibodies (DSA) greater than 1000 MFI. 5. Hepatitis B, Hepatitis C, or HIV positive by PCR. 6. Liver cirrhosis or portal hypertension (successfully treated for Hepatitis B or C are recommended to be evaluated by elastography or liver biopsy to evaluated for cirrhosis). 7. Uncontrolled bacterial, viral or fungal infections (currently taking medication and with progression or no clinical improvement) at time of enrollment. 8. Another cancer in remission less than 2 yrs are not eligible. A history of a previously treated solid tumor whose remission status is 2 yrs or greater and are not receiving tumor directed therapy will be considered eligible. Hormonal therapy as a part of long-term maintenance post-malignancy is allowed. 9. Concurrent participation in another investigational clinical trial(s) with interventions which could influence relapse, GVHD, or viral reactivation. 10. Systemic corticosteroid use at the time of screening. Treatment with hydrocortisone for prevention of transfusion reactions are eligible, but use of methylprednisolone is not allowed. 11. Woman who are pregnant or lactating. 12. Any serious medical or psychiatric illness likely to interfere with participation in this clinical study.