Recipient Inclusion Criteria a. Patients with the following diseases that are histopathologically-confirmed are eligible - Acute myeloid, lymphoid, or mixed phenotype leukemia in complete remission (CR) or CR with incomplete hematologic recovery (CRi) or beyond first complete remission (CR1) without the presence of minimal residual disease - Acute myeloid, leukemia, or mixed phenotype leukemia that is either: - Not in morphologic CR with bone marrow infiltration by leukemic blasts of ≤10%, or - In morphologic CR with evidence of minimal residual disease positivity by either multiparametric flow cytometric analysis or by a nucleic acid-based technique - Primary refractory acute myeloid, lymphoid, or mixed phenotype leukemia - Chronic myelogenous leukemia (accelerated, blast or second chronic phase) - Myelodysplastic syndromes - Myeloproliferative syndromes b. Match to the patient as follows: 1. For Arm A1 (CLOSED): - Availability of a 8/8 or 7/8 HLA-matched donor (related or unrelated) defined by Class I (HLA-A, -B, -C) serologic typing (or higher resolution) and Class II (HLA-DRB1) molecular typing. - If the donor is a 7/8 HLA-match, the mismatch must be a permissive allelic mismatch as assessed by an independent HLA and transplantation expert. 2. For Arm A1 and Arm A3: - Availability of a 8/8 HLA-matched donor (related or unrelated) defined by Class I (HLA-A, -B, -C) serologic typing (or higher resolution) and Class II (HLA-DRB1) molecular typing. 3. For Arm B (CLOSED): • Availability of a haploidentical donor who is a ≥ 4/8 but <7/8 match at HLA-A, -B, -C, and -DRB1 (typed using DNA-based high-resolution methods), with at most one mismatch per locus 4. For Arm C1 (CLOSED) and C2: - Availability of a 8/8 HLA matched donor (related or unrelated) defined by Class I (HLA-A, B, C) serologic typing (or higher resolution) and Class II (HLA DRB1) molecular typing. c. Age ≥ 18 and ≤75 years old at the time of enrollment. For Arm A4, age >/= 18 and </= 78 years of age. d. Left ventricular ejection fraction (LVEF) ≥ 45% e. Diffusing capacity of the lungs for carbon monoxide (DLCO) ≥ 50% f. Calculated creatinine clearance ≥ 50 mL/min or creatinine < 2.0 mg/dL g. SGPT and SGOT ≤ 3 x ULN, unless elevated secondary to disease Total bilirubin ≤ 2 x ULN (patients with Gilbert's syndrome may be included at the discretion of the PI or where hemolysis has been excluded h. Negative serum or urine beta-HCG test in females of childbearing potential within 3 weeks of registration i. Karnofsky performance status ≥ 70% Donor Inclusion Criteria 1. Age ≥ 18 and ≤ 75 years of age 2. Karnofsky performance status of ≥ 70% defined by institutional standards 3. Seronegative for HIV-1 RNA PCR; HIV 1 and HIV 2 ab (antibody); HTLV-1 and HTLV-2 ab; PCR+ or sAg (surface antigen) hepatitis B ; or PCR or sAg negative for hepatitis C; negative for the Treponema palladum antibody Syphillis screen; and negative for HIV-1 and hepatitis C by nucleic acid testing (NAT) within 30 days of apheresis collection. 4. In the case that T palladum antibody tests are positive, donors must: Be evaluated and show no evidence of syphilis infection of any stage by physical exam and history, or Have completed effective antibiotic therapy to treat syphilis, or Have a documented negative non-treponemal test (such as RPR) or in the case of a positive non-treponemal test must be evaluated by an infectious disease expert to evaluate for alternative causes of test positivity and confirm no evidence of active syphilitic disease e. Match to the patient as follows: a. Arm A1(CLOSED): - Must be a related or unrelated, 8/8 or 7/8-HLA match to recipient at HLAA, -B, -C, and -DRB1. If 7/8 HLA-matched, must be with permissive allelic HLA mismatch as assessed by an independent HLA and transplantation expert. b. Arm A2 (CLOSED) and Arm A3 (CLOSED): - Must be a related or unrelated, 8/8 HLA match to recipient at HLA A, B, C, and DRB1 c. Arm B (CLOSED): - Must be a haploidentical donor who is ≥ 4/8 but < 7/8 match at HLA-A, -B, -C, and -DRB1, with at most one mismatch per locus. d. Arm C1 (CLOSED) and Arm C2: - Must be a related or unrelated 7/8 HLA matched to recipient at HLA A, B, C, DRB1 or -DQB1 f. Must be willing to donate PBSC for up two consecutive days g. Female donors of child-bearing potential must have a negative serum or urine beta HCG test within 3 weeks of mobilization h. Capable of undergoing leukapheresis, have adequate venous access, and be willing to undergo insertion of a central catheter should leukapheresis via peripheral vein be inadequate i. Agreeable to 2nd donation of PBPC (or bone marrow harvest) in the event of graft failure j. The donor or legal guardian greater than 18 years of age, capable of signing an IRB approved consent form. k. Meets other criteria for donation as specified by standard NMDP guidelines (NMDP donors) or institutional standards (non-NMDP donors) l. Donors not meeting federal eligibility criterion, may nonetheless be included if either apply as follows per 21 CFR § 1271.65: - The donor is a first-degree or second-degree blood relative of the recipient, or - Documented urgent medical need (DUMN), meaning no comparable human cell product is available and the recipient is likely to suffer death or serious morbidity without the human cell product, as attested by the Investigator or sub-investigator

Recipient Exclusion Criteria 1. Seropositive for any of the following: HIV antibodies; hepatitis B surface antigen (sAg); hepatitis C antibodies 2. Patients deemed candidates for fully myeloablative preparative conditioning regimens d. Candidate for autologous transplant e. Hepatitis B or C with SGPT or SGOT > 3 x ULN f. HIV-positive g. Active uncontrolled bacterial, viral or fungal infection, defined as currently taking antimicrobial therapy and progression of clinical symptoms. h. Uncontrolled CNS disease involvement i. Pregnant or a lactating female j. Positive serum or urine beta-HCG test in females of childbearing potential within 3 weeks of registration k. Psychosocial circumstances that preclude the patient being able to go through transplant or participate responsibly in follow-up care l. Known allergy or hypersensitivity to, or intolerance of, tacrolimus m. Positive anti-donor HLA antibodies against a mismatched allele in the selected donor determined by either: - A positive crossmatch of any titer; or - The presence of anti-donor HLA antibody to any HLA locus n. Any uncontrolled autoimmune disease requiring active immunosuppressive treatment o. Concurrent malignancies or active disease within 1 year, except nonmelanomatous skin cancers that have been curatively resected Donor Exclusion Criteria 1. Evidence of active infection 2. Seropositive for HIV-1 or-2, HTLV-1 or -2 3. Medical, physical, or psychological reason that would place the donor at increased risk for complications from growth factor or leukapheresis 4. Lactating female