Orca-T Following Chemotherapy and Total Marrow and Lymphoid Irradiation for the Treatment of Acute Myeloid Leukemia, Acute Lymphoblastic Leukemia or Myelodysplastic Syndrome

Inclusion Criteria: * Documented informed consent of the participant * Agreement to allow the use of archival tissue from diagnostic bone marrow biopsies * If unavailable, exceptions may be granted with study primary investigator (PI) approval * Age: 60-75 years * Karnofsky performance status ≥ 70 * Eligible patients will have a histopathological confirmed diagnosis of hematologic malignancy in one of the following categories: * Acute myelogenous leukemia: * Patients with de novo or secondary disease in CR1 or more with European LeukemiaNet (ELN) intermediate or adverse risk category, or * Patients with active disease * Morphologically; or * Minimal residual disease (MRD) + (flow cytometry of ≥ 0.1%, next generation sequencing \[NGS\] or cytogenetics) * Acute lymphoblastic leukemia (ALL): * Patients with de novo or secondary disease according to National Comprehensive Cancer Network (NCCN) guidelines for ALL hypoploidy (\< 44 chromosomes); t(v;11q23): MLL rearranged; t(9;22) (q34;q11.2); complex cytogenetics (5 or more chromosomal abnormalities); high white blood cell (WBC) at diagnosis (≥ 30,000 for B lineage or ≥ 50,000 for T lineage); iAMP21loss of 13q, and abnormal 17p; or * Patients with active disease: * Morphologically; or * MRD+ (flow cytometry of ≥ 0.1%, or cytogenetics) * Myelodysplastic syndrome in high-intermediate (int-2) and high risk categories per International Prognostic Scoring System Risk (IPSSR) * Serum direct (conjugated) bilirubin ≤ 2.0 mg/dl performed within 30 days prior to day 1 * Serum glutamic oxaloacetic transaminase (SGOT) and serum glutamic pyruvic transaminase (SGPT) ≤ 2.5 times the institutional upper limits of normal performed within 30 days prior to day 1. Patients with Gilberts disease are allowed * Creatinine clearance of ≥ 60 mL/min per 24 hour urine test or the Cockcroft-Gault formula performed within 30 days prior to day 1 * Ejection fraction measured by echocardiogram or MUGA ≥ 50% performed within 30 days prior to day 1 * If able to perform pulmonary function tests: forced expiratory volume in 1 second (FEV1), forced vital capacity (FVC) and carbon monoxide diffusing capability (DLCO) (diffusion capacity) ≥ 50% of predicted (corrected for hemoglobin). If unable to perform pulmonary function tests: oxygen (O2) saturation \> 92% on room air performed within 30 days prior to day 1 * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test performed within 30 days prior to day 1. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential\* to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy. * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) * PATIENTS: Patients should have discontinued all previous intensive therapy, chemotherapy or radiotherapy for 2 weeks prior to commencing therapy on this study NOTE: Low dose chemotherapy or maintenance chemotherapy given within 7 days of planned study enrollment is permitted. These include hydroxyurea, 6-meraptopurine, oral methotrexate, vincristine, oral etoposide, and tyrosine kinase inhibitors (TKIs). FLT-3 inhibitors can also be given up to 3 days before conditioning regimen.) All patients with prior radiation treatment to the lung, liver, and kidney will be excluded. For other scenarios of prior radiation treatment, up to 2000 cGy at 2 Gy per day will be allowed. Inclusion of patients with previous radiation exposure will be determined based on the radiation oncologist medical doctor (MD) evaluation and judgment * DONORS: All candidates for this study must have an human leukocyte antigen (HLA) (A, B, C, and DR) identical sibling who is willing to donate mobilized peripheral blood stem cells or have a 10/10 (A, B, C, DR and DQ) allele matched unrelated donor (DQ or DP mismatch is allowed per discretion of the principal investigator), or haploidentical donor. City of Hope (COH) standard operating procedures (SOP) (B.001.11) will be used for allogeneic donor evaluation, selection, and consent. Donor screening will be in compliance with all requirements of Food and Drug Administration (FDA) regulation 21 Code of Federal Regulations (CFR) Part 1271 including donor screening for COVID-19 exposure or infection Exclusion Criteria: * PATIENTS: Prior allogeneic stem cell transplant * PATIENTS: More than 3 prior lines of intensive chemotherapy, where the regimen intent was to induce remission * PATIENTS: Receiving any other investigational agents or concurrent biological, intensive chemotherapy or radiation therapy for the previous 2 weeks from conditioning NOTE: Low dose chemotherapy or maintenance chemotherapy given within 7 days of planned study enrollment is permitted. These include: Hydroxyurea, 6-meraptopurine, oral methotrexate, vincristine, oral etoposide, and tyrosine kinase inhibitors (TKIs). FLT-3 inhibitors can also be given up to 3 days before conditioning regimen * PATIENTS: History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent * PATIENTS: Having any uncontrolled illness including ongoing or active bacterial, viral or fungal infection requiring antibiotics * PATIENTS: Patients with other active malignancies are ineligible for this study, other than non-melanoma skin cancer, in situ cervical cancer and prostate cancer. Patients with prior history of localized prostate cancer treated with curative intent regardless of time from the treatment to study entry, and patients with prostate cancer receiving active surveillance not requiring therapy are eligible * PATIENTS: The recipient has a medical problem or neurologic/psychiatric dysfunction which would impair his/her ability to be compliant with the medical regimen and to tolerate transplantation or would prolong hematologic recovery which in the opinion of the principal investigator would place the recipient at unacceptable risk * PATIENTS: Females only: Pregnant or breastfeeding * PATIENTS: Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * PATIENTS: Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)