Naive T Cell Depletion for Preventing Chronic Graft-versus-Host Disease in Children and Young Adults With Blood Cancers Undergoing Donor Stem Cell Transplant

Inclusion Criteria: * The patient must have one of the following diagnoses and be considered to be an appropriate candidate for allogeneic HCT by the study site principal investigator (PI): * Acute lymphoblastic leukemia (ALL) with \< 5% marrow blasts. * Acute myeloid leukemia (AML) with \< 25% marrow blasts. * Other acute leukemia (OAL) or related neoplasm (including but not limited to acute biphenotypic leukemia \[ABL\], ambiguous lineage \[ALAL\], mixed phenotype acute leukemia \[MPAL\], blastic plasmacytoid dendritic cell neoplasm \[BPDCN\], acute undifferentiated leukemia \[AUL\], lymphoblastic lymphoma, Burkitt leukemia/lymphoma, mast cell leukemia, chronic monocytic leukemia \[CML\] with blast crisis or other chronic myeloproliferative neoplasm) with \< 5% marrow blasts. * Myelodysplastic syndrome (MDS) with excess blasts (EB-1 and EB-2) and has received cytotoxic induction chemotherapy (excluding small molecule inhibitors and de-methylating agents) * Age 6 months to 26 years at the time informed consent is obtained using the Informed Consent to Participate in a Research Study form * Matched related donor (MRD) or matched unrelated donor (MUD) (defined as 8/8 match for human leukocyte antigen \[HLA\]-A, -B, -C, -DRB1). * Planned product type for infusion is PBSC or BM (i.e. not cord blood): * For feasibility phase, planned product type for infusion must be PBSC. * For RCT, planned product type must be PBSC or BM. * Karnofsky or Lansky score \>= 60%. * Le…