CD8 Depleted, Non-engrafting, HLA Mismatched Unrelated Infusion With MDS and Secondary AML

Inclusion Criteria: Myelodysplastic Syndrome (MDS) having failed hypomethylating agent (HMA) therapy cohort: * Age 18-79 years, inclusive * Pathologically confirmed MDS or myelodysplastic/myeloproliferative overlap (MDS/MPN) * IPSS-R score intermediate, high or very high * Must have failed therapy with an HMA (defined as lack of response by International Working Group criteria (1) or intolerance of the drug) Secondary Acute Myeloid Leukemia (sAML): * Pathologically confirmed AML according to World Health Organization (WHO) criteria * Evidence of an antecedent hematologic disorder (AHD) prior to acute leukemia including a known prior diagnosis of MDS, MPN or MDS/MPN or data suggestive of an AHD such as cytopenias, fibrosis, macrocytic anemia, cellular or dysplasia at or prior to the time of diagnosis. If available, MDS-defining karyotypes (-7/del(7q), -5/del(5q), del(13q), del(11q), del(12p), t(12p), del(9q), idic(X)(q13), t(17p) (unbalanced translocations) or i(17q) (ie, loss of 17p), t(11;16)(q23;p13.3), t(3;21)(q26.2;q22.1), t(1;3)(p36.3;q21), t(2;11)(p21;q23), inv(3)(q21q26.2), t(6;9)(p23;q34)) or somatic mutations in multiple genes including p53, TET2, JAK2, CALR, MPL, ASXL1, RUNX1, SRSF2, SF3B1, U2AF1, ZRSR2, ASXL1, EZH2, BCOR, or STAG2 would also confirm eligibility. * Age 60-79 years, inclusive * May be previously untreated For both cohorts: * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Deemed eligible to receive cytotoxic chemotherapy * Creatinine clearance (CrCl)\>50ml/min * Total bilirubin \<2 mg/dL (except for patients with Gilbert's disease), AST and ALT \< 3x ULN * Left Ventricular Ejection Fraction ≥ 50% * Willing and able to participate in study assessments Exclusion Criteria: * Patients who have had systemic chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier. Hydroxyurea during this period may be given as a bridging therapy to maintain disease stability while awaiting treatment. Intrathecal chemotherapy within this time frame is permitted. Intrathecal chemotherapy may be continued during protocol therapy in order to consolidate or maintain a central nervous system (CNS) remission, but not to treat active CNS disease * Acute promyelocytic leukemia, or the presence of t(15;17) * Patients receiving any other investigational agents * Uncontrolled concurrent illness including, but not limited to, ongoing and uncontrolled infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because there is an unknown but potential risk for adverse events in the fetus. Breastfeeding should be discontinued if the mother is treated. These potential risks may also apply to other agents used in this study * Patients who have any debilitating medical or psychiatric illness that would preclude their giving informed consent or their receiving optimal treatment and follow-up * Patients with a poor functional status of ECOG 3-4, or otherwise deemed unfit to tolerate induction chemotherapy. * Patients with blastic transformation of chronic myelogenous leukemia are ineligible * Exposure to a humanized mouse chimeric antibody, as this could sensitize patients to components of the CD8 depletion column that may be present in small amounts in the cell product * Prior allogenic hematopoietic cell transplant