IS-free Treg HaploHCT

Inclusion Criteria: * Cohort A: Histologically confirmed disease in the prior 4 weeks, despite at least 1 prior line of therapy (e.g., 3+7 chemotherapy, HMA therapy): Rel/ref AML (de novo or secondary) with ≥5% blasts in BM (or extramedullary sites); MDS EB-2 (BM ≥10% blasts, PB 5-19% blasts). * Cohort B: Ultra high-risk AML or MDS that meets definition of 'Myeloid Neoplasms with mutated TP53' per 2022 International Consensus Classification (Appendix L) regardless of response * Cohort C: Ultra high-risk AML or MDS that meets definition of 'Myeloid Neoplasms with multi-hit or complex karyotype (CK+) mutated TP53' per 2022 International Consensus Classification (Appendix L) with response: AML (de novo or secondary) with \<5% blasts in BM; MDS with \<10% blasts in BM or PB. * Available haploidentical HLA-matched (-A, -B, -C, -DRB1) related donor aged 18-65 years. * Age ≥18 to 65 years for Cohort A and B. Age ≥18 to 75 years for Cohort C. Because no dosing or adverse event data are currently available on the use of IS-free haploHCT in participants \<18 years of age, children are excluded from this study but will be eligible for future pediatric trials. * ECOG performance status ≤2 (Karnofsky ≥60, see Appendix A). * Adequate organ and marrow function as defined below: * Pulmonary Function: FEV1, FVC and DLCO ≥ 60% of predicted (corrected for hemoglobin) * Cardiac Ejection Fraction ≥ 45%, and no evidence of pulmonary hypertension * Hepatic: Total bilirubin within normal institutional limits (exception permitted in Gilbert's Syndrome after discussion with study PI, on a case-by-case basis); and AST (SGOT)/ALT (SGPT) \<2x institutional upper limit of normal * Renal: Serum Creatinine within normal institutional limits or creatinine clearance \>50 mL/min/1.73 m2 (see Appendix B) for participants with creatinine levels above institutional normal. * The effects of IS-free haploHCT on the developing human fetus are unknown. For this reason and because radiation and chemotherapeutic agents are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and a minimum of 4 months after completion of study. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Participants who have had cytotoxic chemotherapy or radiotherapy within 2 weeks (4 weeks for nitrosoureas or mitomycin C) prior to entering the study. Use of hydroxyurea, HMA, e.g., azacytidine, decitabine) and/or FDA-approved novel targeted agents (e.g., venetoclax, FLT-3 inhibitors, IDH 1/2 inhibitors) are permitted up to a day prior to start of HCT conditioning. * Participants who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual non-hematologic toxicities \> Grade 1) with exception of alopecia, unless cleared by study PI. * Participants who received Mylotarg or other therapies associated with increased risk of hepatic veno-occlusive disease (VOD) or have known prior or active VOD. All novel therapies will be reviewed with PI. * Participants who are receiving any other investigational agents within 21 days (or 5 half-lives) prior to study entry, whichever is longer, unless cleared by the study PI. * Participants with extramedullary disease at immune privileged sites (e.g., CNS, testes, eye) are excluded, as these sites are less susceptible to the curative graft vs. leukemia effect of HCT. * Myocardial infarction within 2 years prior to enrollment. * Venous thromboembolic event (VTE) of DVT/ PE within 1 year prior to enrollment, unless approved by study PI. Patients with line-associated DVT within the past year may be enrolled if they have completed anticoagulation therapy. * Stroke or transient ischemic attack (TIA) within 1 year prior to enrollment. * History of bleeding peptic ulcer disease, erosive gastritis, intestinal perforation or clinically significant gastrointestinal (GI) hemorrhage or hemoptysis within the prior 6 months. * Patients with a history of thrombotic microangiopathy (TMA) or hemolytic uremic syndrome/thrombotic thrombocytopenic purpura (HUS/TTP). * History of life-threatening reactions to iron infusions or murine antibody-containing products. * Known donor-specific antibodies (DSA) in the recipient of clinical significance (e.g., requiring DSA depletion with plasmapheresis, rituximab) are excluded. * Inability to withhold agents that may interact with hepatic cytochrome P450 enzymes involved in cyclophosphamide and/or thiotepa metabolism (see Section 5.5) during day -10 through day -5. It is acceptable use alternative non-interacting medications during this period, and then restart prior medications * Participants with uncontrolled bacterial, viral or fungal infections (i.e., currently taking medications with progression of clinical symptoms or signs). * Recipients of prior allogeneic or autologous hematopoietic cell transplantation, or solid organ transplantation. * Prior radiation exposure or other medical condition (e.g., Fanconi syndrome) that precludes use of myeloablative radiation (TMLI). * HIV-positive participants on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with the multiple agents used routinely in myeloablative allogeneic stem cell transplantation. In addition, these individuals are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in participants receiving combination antiretroviral therapy when indicated. * Participants seropositive for hepatitis B or C infection are ineligible as they are at high risk of lethal treatment-related hepatotoxicity after myeloablative HCT. * Participants with psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant women are excluded from this study because radiation and conditioning chemotherapy has the potential for teratogenic or abortifacient effects. A negative pregnancy test is required for females of childbearing potential. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with IS-free haploHCT breastfeeding should be discontinued if the mother is treated with IS-free haploHCT. * Participants with a history of another non-hematologic malignancy are ineligible except for the following circumstances: Individuals with a history of other malignancies are eligible if they have been disease-free for at least 5 years and are deemed by the investigator to be at low risk for recurrence of that malignancy. Individuals with the following cancers are eligible if diagnosed and treated within the past 5 years: cervical cancer in situ, and basal cell or squamous cell carcinoma of the skin.