QUILT-3.034: Non-Myeloablative TCRa/b Deplete Haplo HSCT With Post ALT-803 for AML

Inclusion Criteria: * Age ≥18 to ≤70 years * Meets one of the following disease and risk categories: * High-Risk Acute Myeloid Leukemia (AML) with predicted risk of relapse higher than 30%, which includes, but not limited to the following: * Patients in morphological remission (CR1 or beyond) with minimal residual disease as quantified either by flow cytometry, or by cytogenetics or molecular markers. * Patients with the following karyotypes in morphological CR or CRi: ELN-Intermediate I, Adverse, ELN-Intermediate-II. (18) (Examples include monosomal karyotype, complex karyotype, mutant p53, mutant RUNX1, mutant ASXL1, mutant FLT3-ITD, mutant DNMT3A, Inversion 3, T(6:9), KIT mutated core binding factor AML) * Treatment-Related AML and Secondary AML in morphological remission (CR1 or beyond) with minimal residual disease as quantified either by flow cytometry, or by cytogenetics or molecular markers * Myelodysplastic Syndrome (MDS) with \< 5% blasts by morphology and meets at least one of the following: * Received intensive induction chemotherapy (i.e. 7+3 or MEC) OR * Progression after 4 cycles of hypomethylating agents * The donor and recipient must be HLA identical for at least one haplotype (using high resolution DNA based typing) at the following genetic loci: HLA-A, HLA-B, HLA-C, and HLA-DRB1 * Karnofsky performance status ≥ 60% (appendix IV) * Adequate organ function within 14 days of study registration (30 days for pulmonary and cardiac) defined as: * Hepatic: AST and ALT \< 3 x upper limit of institutional normal * Renal: estimated glomerular filtration rate (GFR) ≥ 40 mL/min/1.73m2 * Pulmonary: oxygen saturation ≥ 90% on room air with no symptomatic pulmonary disease. If symptomatic or prior known impairment DLCOcor ≥ 40%. * Cardiac: LVEF ≥ 40% by echocardiography, MUGA, or cardiac MRI, no uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities * Able to be off prednisone or other immunosuppressive medications for at least 3 days prior to transplant (excluding preparative regimen pre-medications) * Sexually active females of child bearing potential and males with partners of child bearing potential must agree to use effective contraception during therapy and for 4 months after completion of therapy * Voluntary written consent prior to the performance of any research related procedures Exclusion Criteria: * Acute leukemias of ambiguous lineage * Allogeneic transplant for AML within the previous 6 months (no time limit for autologous transplant) * Active CNS disease - if a history of AML related CNS involvement, screening CSF analysis must be negative * Pregnant or breastfeeding - The agents used in this study include those that fall under Pregnancy Category D - have known teratogenic potential. Women of child bearing potential must have a negative pregnancy test at screening * Active autoimmune disease requiring systemic immunosuppressive therapy * History of severe asthma and currently on systemic chronic medications (mild asthma requiring inhaled steroids only is eligible) * New or progressive pulmonary infiltrates on screening chest x-ray or chest CT scan unless cleared for study by Pulmonary. Infiltrates attributed to infection must be stable/improving (with associated clinical improvement) after 1 week of appropriate therapy (4 weeks for presumed or documented fungal infections). * Uncontrolled bacterial, fungal or viral infections including HIV-1/2 or active hepatitis C/B - chronic asymptomatic viral hepatitis is allowed * Active concomitant second malignancy (i.e. has required treatment in the previous 6 months) * Known hypersensitivity to any of the study agents * Received any investigational drugs within the 14 days before 1st dose of fludarabine