TCRαβ-depleted Progenitor Cell Graft With Early Memory T-cell DLI, Plus Selected Use of Blinatumomab, in naïve T-cell Depleted Haploidentical Donor Hematopoietic Cell Transplantation for Hematologic Malignancies

Inclusion Criteria: Recipient: * Age less than or equal to 21 years * High risk hematologic malignancy whereas allogeneic transplantation is the current standard of care. This includes (but is not limited to): * High risk ALL in CR1 or CR2, * any ALL in CR3 or subsequent; * AML in high risk CR1 (AML diagnosis includes myeloid sarcoma), * any AML in CR2 or subsequent, * any therapy related AML; * MDS (primary or secondary), * NK cell, biphenotypic, or undifferentiated leukemia/lymphoma in CR1 or subsequent; * CML in accelerated phase, or in chronic phase with persistent molecular positivity or intolerance to tyrosine kinase inhibitor, or a history of blast crisis. * If prior CNS leukemia, it must be treated and in CNS CR * Left ventricular ejection fraction \> 40%, or shortening fraction ≥ 25% * Creatinine clearance (CrCl) or glomerular filtration rate (GFR) ≥ 50 ml/min/1.73m2 * Forced vital capacity (FVC) ≥ 50% of predicted value; or pulse oximetry ≥ 92% on room air if patient is unable to perform pulmonary function testing * Karnofsky or Lansky (age dependent) performance score ≥ 50 (See APPENDIX A) * Bilirubin ≤ 3 times the upper limit of normal for age * Alanine aminotransferase (ALT) or Aspartate aminotransferase (AST) ≤ 5 times the upper limit of normal for age Donor: * At least single haplotype matched (≥ 4 of 8) family member * At least 18 years of age * HIV negative * Regarding donation eligibility, is identified as either: * Completed the process of donor eligibility determination as outlined in 21 CFR 1271 and agency guidance; OR * Does not meet 21 CFR 1271 eligibility requirements, but has a declaration of urgent medical need completed by the principal investigator or physician sub-investigator per 21 CFR 1271 Exclusion Criteria: Recipient: * Has a suitable HLA-identical sibling or suitable 12/12 (HLA-A, B, C, DRB1, DQB1, and DPB1) HLA-matched unrelated donor available in an appropriate time frame. * Any other active malignancy other than the one for which this HCT is indicated * Received a prior allogeneic HCT at any time * Received an autologous HCT within the previous 6 months * Pregnant, if female is of childbearing potential, negative test must be confirmed by serum or urine pregnancy test within 14 days prior to enrollment * Breast feeding * Any current uncontrolled bacterial, fungal or viral infection Donor: * Pregnant, negative test must be confirmed by serum or urine pregnancy test within 14 days prior to enrollment if female * If female, breast feeding