Safety/PK Study of Gene Modified Donor T Cell Infusion in Children With Recurrent Hem Malignancies After Allo Transplant

Inclusion Criteria: * Patients aged \< 18 * Clinical diagnosis of one of the following pediatric hematological malignancies: * High-risk Acute Leukemia (Acute lymphoblastic leukemia \[ALL\] or acute myeloid leukemia \[AML\]) in any CR * Acute Leukemia that is minimal residual disease (MRD) positive at \> 1copy per 1 x 10,000 reference copies pre-HSCT * Myelodysplastic Syndrome (MDS) * Hodgkin or Non-Hodgkin lymphomas * Other high-risk hematological malignancy in CR eligible for stem cell transplantation per institutional standard * Patients with a hematological malignancy who have received a prior allogeneic HSCT * Patients with on-treatment relapse of AML within 6 months of initial CR * Patients relapsing within 6 months of initial diagnosis of hematological malignancy. * Planned or previous treatment of hematological malignancy with one of the following: * Matched related HSCT * Mismatched related HSCT * For patients who have received a transplant, occurrence of one of the following \> 30 days post-HSCT: * Minimal residual disease (MRD) positive at \> 1 copy per 1 x 10,000 reference copies post-HSCT * Decreasing donor chimerism detected on two bone marrow biopsies or peripheral blood analyses at a \> 7-day interval * Recurrent disease * Life expectancy \>10 weeks; * Signed donor and patient/guardian informed consent; * For mismatched related donor recipients, a minimum genotypic identical match of 5/10 is required, as determined by high resolution typing, at least one allele of each of the following genetic loci must be matched: HLA-A, HLA-B, HLA-C, HLA- DRB1, and HLA-DQB1. * Performance status: Karnofsky/Lansky score \> 70%. * Adequate organ function as measured by: * High-risk Acute Leukemia (Acute lymphoblastic leukemia \[ALL\] or acute myeloid leukemia \[AML\]) in any CR * High-risk Acute Leukemia (Acute lymphoblastic leukemia \[ALL\] or acute myeloid leukemia \[AML\]) in any CR * Hepatic: direct bilirubin ≤ 3x ULN, or AST/ALT ≤ 5x ULN. * Bone marrow; * \> 25% donor T cell chimerism * ANC \>1 x 10\^9/L. * Cardiac: LVEF at rest \>45%. * Pulmonary: FEV 1, FVC, DLCO (diffusion capacity for CO) \> 50% predicted (corrected for hemoglobin); for children who are unable to perform pulmonary function tests due to age or developmental ability, there must be no evidence of dyspnea or no need for supplemental oxygen as evidenced by 02 saturation ≥ 92% on room air. * Hepatic: direct bilirubin ≤ 3x ULN, or AST/ALT ≤ 5x ULN. * Renal: creatinine clearance ≤ 2x of ULN for age Exclusion Criteria: ≥ Grade II acute GVHD or moderate to severe chronic GVHD due to a previous allograft at the time of screening; * Active CNS involvement by malignant cells (\< 2 months prior to time of consent); * Current uncontrolled bacterial, viral or fungal infection (currently taking medication with evidence of progression of clinical symptoms or radiologic findings). * Positive HIV serology or viral RNA; * Pregnancy (positive serum βHCG test) or breast-feeding female; * Patients of reproductive age unwilling to use effective forms of birth control or abstinence for a year after BPX-501 T cell infusion.