MCW Alpha/Beta T-Cell and B-Cell Depletion With Targeted ATG Dosing

Inclusion Criteria: 1. Patient age \< 25 years. Both genders and all races eligible. 2. Disease eligibility * Acute myeloid leukemia, primary or secondary - Disease status: MRD negative (flow MRD ≤ 0.1%) * Myelodysplasia * Acute lymphoblastic leukemia - Disease status: MRD negative * Chronic myelogenous leukemia - Disease status: chronic phase, accelerated phase or blast crisis now in second chronic phase * Mixed lineage or biphenotypic acute leukemia- Disease status: MRD negative * Lymphoblastic lymphoma - Disease status: in remission * Burkitt's lymphoma/leukemia - Disease status: in remission * Lymphoma after relapse - Disease status: in remission * Other malignant hematologic diseases in remission (to be approved by PI) 3. Karnofsky Performance Status ≥ 60% for patients 16 years and older and Lansky Play Score ≥ 60 for patients under 16 years of age (Appendix 1) 4. Evaluation of organ status as per MCW BMT SOP 5. Infectious disease criteria: No active untreated infection. Patients with possible fungal infections must have had at least 2 weeks of appropriate anti-fungal antibiotics and be asymptomatic. 6. Signed consent by parent/guardian or able to give consent if ≥18 years. 7. Negative pregnancy test for patients capable of childbearing potential 8. Sexually active patients capable of child-bearing potential must agree to use adequate contraception (diaphragm, birth control pills, injections, intrauterine device \[IUD\], surgical sterilization, subcutaneous implants, or abstinence, etc.) for the duration of treatment. Sexually active men must agree to use barrier contraceptive for the duration of treatment. Donor Eligibility: 1. Unrelated donor meets National Marrow Donor Program criteria for donation 2. Infectious disease testing 3. MCW BMT procedures apply for determining donor eligibility, including donor screening and testing for relevant communicable disease agents and diseases. 4. Only Peripheral blood stem cells will be used for stem cell source on this study therefore donor must be willing to undergo G-CSF mobilization and stem cell apheresis. Donor matching. High resolution typing at all loci to be performed. 5. Unrelated Donor: a. HLA typing of at least 10 alleles is required. Donor must be matched at 9/10 or 10/10 alleles (HLA A, B, C, DRB1, DQB1).Donor and collection center willing to undergo mobilization and apheresis 6. Haploidentical Related Donor: 1. Haploidentical parent or other related donor: Minimum match level full haploidentical (at least 5/10; HLA A, B, C, DRB1, DQB1 alleles), but use of haploidentical donors with extra matches (e.g. 6, 7, or 8/10) encouraged. Exclusion Criteria: 1. Patients who do not meet disease, organ, or infectious criteria. 2. No suitable donor 3. Pregnant or lactating patients are ineligible as many of the medications used in this protocol could be harmful to unborn children and infants 4. Receiving concomitant chemotherapy, radiation therapy; immunotherapy or other anti-cancer therapy for treatment of disease other than is specified in the protocol. Maintenance or other post-HCT therapy can be considered after discussion with the study PI. 5. Participating in a concomitant Phase 1 or 2 study involving treatment of disease 6. Active malignancy other than eligible disease specified in the protocol. Patients with prior malignancy can be eligible as long as at least 1 year post treatment for that malignancy.