Phase 1-2 MAHCT w/ TCell Depleted Graft w/ Simultaneous Infusion Conventional and Regulatory T Cell

Recipient Inclusion Criteria 1. Patients with the following diseases that are histopathologically confirmed are eligible * Acute leukemia, primary refractory or beyond CR1, or minimal residual disease (MRD) positivity. * High risk acute myeloid leukemia in CR1 with any of the following features: * Complex karyotype(≥3 clonal chromosomal abnormalities) * Any of the following high risk chromosomal abnormalities: * Monosomal karyotype (-5, 5q-, -7, 7q-) * t(11q23), t(9;11), inv(3), t(3;3) t(6;9) t(9;22) * Normal karyotype with fms-like tyrosine kinase 3 (FLT3)-ITD mutation * Other high risk features as determined by molecular studies, or clinical presentation as assessed by the treating physician * Chronic myelogenous leukemia (accelerated, blast or second chronic phase) * Myelodysplastic syndromes * Myeloproliferative syndromes * Non-Hodgkin lymphoma with poor risk features not suitable for autologous HCT 2. Age ≥18 yo and ≤ 60 yo for patients in Cohort 1 only. At the start of Cohort 2A and beyond, eligibility will be expanded to allow pediatric patients age ≥ 13 yo. 3. Cardiac ejection fraction ≥ 45% 4. Lung diffusion capacity ≥ 50% 5. Calculated creatinine clearance ≥ 50 cc/min 6. Serum glutamic-pyruvic transaminase( SGPT) and serum glutamic-oxaloacetic transaminase (SGOT) ≤ 3.0 x ULN (Upper limit of normal), unless elevated secondary to disease. 7. 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 8. Availability of a HLA matched donor (related or unrelated) defined by Class I (HLA-A and B) serologic typing (or higher resolution) and Class II (HLA DRB1) molecular typing. An HLA matched donor is defined for this study to be a sibling that is HLA matched 6/6; or an unrelated donor that is HLA matched 6/6 or 5/6. A sibling may be a "half sibling." 9. Karnofsky performance status ≥70% Recipient Exclusion Criteria 1. Seropositive for any of the following: HIV ab; hepatitis B sAg; hepatitis C ab 2. Prior myeloablative therapy or hematopoietic cell transplant 3. Candidate for autologous transplant 4. HIV positive 5. Active uncontrolled bacterial, viral or fungal infection, defined as currently taking antimicrobial therapy and progression of clinical symptoms. 6. Uncontrolled central nervous system (CNS) disease involvement 7. Pregnant or a lactating female 8. Positive serum or urine beta human chorionic gonadotropin (HCG) test in females of childbearing potential within 3 weeks of registration 9. Psychosocial circumstances that preclude the patient being able to go through transplant or participate responsibly in follow up care Donor Inclusion Criteria 1. Age ≥13 yo and ≤ 75 years 2. Karnofsky performance status of ≥ 70% defined by institutional standards 3. Seronegative for HIV 1 RNA (polymerase chair reaction (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 for hepatitis C; negative for the Treponema pallidum antibody Syphilis screen; and negative for HIV 1 and hepatitis C by nucleic acid testing (NAT) within 30 days of apheresis collection. In the case that T pallidum antibody tests are positive, donors must: * Be evaluated and show no evidence of syphilis infection of any stage by physical exam and history * Have completed effective antibiotic therapy to treat syphilis * 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 4. Must be 6/6 matched sibling donor as determined by HLA typing 5. Female donors of child-bearing potential must have a negative serum or urine beta-HCG test within three weeks of mobilization 6. 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 7. Agreeable to 2nd donation of Peripheral blood stem cell (PBPC) (or bone marrow harvest) in the event of graft failure 8. The donor or legal guardian greater than 18 years of age, capable of signing an institutional review board (IRB-approved consent form. Donor Exclusion Criteria 1. Evidence of active infection or viral hepatitis 2. HIV positive 3. Medical, physical, or psychological reason that would place the donor at increased risk for complications from growth factor or leukapheresis 4. Lactating female