Trial for Patients w/ Advanced Hematologic Malignancies Undergoing Allogeneic HCT

Inclusion Criteria: 1. Eligible diseases: * Acute myeloid, lymphoid or mixed phenotype leukemia in complete remission (CR) or CR with incomplete hematologic recovery (CRi) as defined in Section 6.1.3; with or without the presence of known minimal residual disease, or * Myelodysplasic syndrome (MDS) myelodysplastic syndromes eligible for alloHSCT and/or treatment-related MDS \<10% blasts 2. Age ≥ 18 and ≤ 70 years at the time of enrollment. 3. Eligible for myeloablative alloHCT including one of two the myeloablative conditioning regimens (fractionated total body irradiation plus cyclophosphamide or busulfan, fludarabine, and thiotepa) 4. Has a related or unrelated donor available who is 7/8 match (single allele mismatched) at HLA-A, -B, -C, and -DRB1, all typed using DNA-based high-resolution methods. 5. Estimated glomerular filtration rate (eGFR) ≥ 50 mL/minute or creatinine \< 2 mg/dL. 6. Cardiac ejection fraction at rest ≥ 45% or shortening fraction of ≥ 27% by echocardiogram or radionuclide scan (MUGA). 7. Diffusing capacity of the lung for carbon monoxide (DLCO) (adjusted for hemoglobin) ≥ 50%. 8. Total bilirubin \< 2 times upper limit of normal (ULN) (patients with Gilbert's syndrome may be included once hemolysis has been excluded). 9. Ability to understand and the willingness to provide written informed consent. 10. Negative serum or urine beta-HCG test in females of childbearing potential (FCBP) within 3 weeks of enrollment. A female of childbearing potential (FCBP) is a female who: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). 11. Able to give informed consent. Legal authorized representative (LAR) is permitted if subject is cognitively able to provide verbal assent. 12. Karnofsky Performance Score ≥70% Exclusion Criteria: 1. Prior allogeneic HCT. 2. Currently receiving corticosteroids or other immunosuppressive therapy. Topical corticosteroids or oral systemic corticosteroid doses less than or equal to 10 mg/day are allowed. 3. Planned donor lymphocyte infusion (DLI). 4. Planned pharmaceutical in vivo or ex vivo T cell depletion, e.g., post-transplant cyclophosphamide (Cy), peri-transplant anti-thymocyte globulin (ATG), or alemtuzumab. For patients that have previously been exposed to a T cell-depleting agent, a 5 half-life washout of the agent must occur prior to planned Day 0 (day of infusion of Orca-T HSPC and Tregs ). 5. Recipient positive anti-donor HLA antibodies against a mismatched allele in the selected donor determined by either: 1. Positive crossmatch test of any titer (by complement-dependent cytotoxicity or flow cytometric testing), or 2. Presence of anti-donor HLA antibody to any of the following HLA loci: HLA-A, -B, -C, -DRB1, -DQB1, -DQA1, -DPB1, or -DPA1, with mean fluorescence intensity (MFI) \>1000 by solid phase immunoassay. 6. Uncontrolled bacterial, viral, or fungal infections (currently taking antimicrobial therapy and with progression or no clinical improvement) at time of enrollment including known, active tuberculosis infection. 7. Seropositive for HIV-1 or -2, HTLV-1 or -2, Hepatitis B sAg, and/or Hepatitis C antibody. \*History of hepatitis B or hepatitis C is permitted if viral load is undetectable per quantitative PCR and/or NAT. In this case, monitoring for hepatitis B or hepatitis C by PCR at 3, 6, and 12 months is recommended. 8. Known allergy or hypersensitivity to, or intolerance of, any investigational agent or ingredient therein, or planned GVHD prophylactic medications. 9. Documented allergy or hypersensitivity to iron dextran or bovine, murine, algal or Streptomyces avidinii proteins. 10. Any uncontrolled autoimmune disease requiring active immunosuppressive treatment. 11. Concurrent malignancy diagnosed within 12 months of enrollment, except non-melanoma skin cancers that have been curatively resected. 12. Females of childbearing potential (FCBP) or men who have sexual contact with FCBP unwilling to use effective forms of birth control or abstinence for one year after transplantation. (FCBP definition: A female of childbearing potential (FCBP) is a female who: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). 13. History of myocardial infarction, cardiac angioplasty or stenting, unstable angina, or other clinically significant cardiac disease within 12 months of enrollment. History of stroke or pulmonary embolism within 6 months of enrollment. 14. Any serious medical condition or abnormality in clinical laboratory tests that, in the investigator's judgment, precludes the recipient's safe participation in and completion of the study, or which could affect compliance with the protocol or interpretation of results.