Optimized Cord Blood Transplantation for the Treatment of Patients With High-risk Hematologic Malignancies Who Have Relapsed After First Allogeneic Stem Cell Transplantation

Inclusion Criteria: 1. Patient aged 0-60 y/o at the time of consent. Adult is defined as patients 18 years of age or older at the time of consent. 2. Patient must have relapsed \>100 days since first transplant. 3. Diagnosis and Disease Status: a. Acute myelogenous leukemia (AML): i. Patients in morphologic remission (\<5% blasts) at the time of transplant, with or without persistent cytogenetic, flow cytometric, or molecular aberrations, or those with hypocellular marrows at time of transplant, are eligible. b. Acute lymphoblastic leukemia (ALL): i. Patients in morphologic remission with less than 5% blasts at time of transplant, with or without persistent cytogenetic, flow cytometric or molecular aberrations, or those or who have hypocellular bone marrows, are eligible. c. Other acute leukemias: i. Acute leukemias of ambiguous lineage or mixed phenotype in morphologic remission with less than 5% blasts at time of transplant, with or without persistent cytogenetic, flow cytometric or molecular aberrations, or those who have hypocellular bone marrows, are eligible. d. Myelodysplastic Syndromes (MDS) or CMML without myelofibrosis. i. Includes MDS with any IPSS risk category. 4. Prior treatment: a. To be eligible for this study, patients need to have received one prior allogeneic stem cell transplantation. 5. Karnofsky score equal or greater than 70% for patients aged 16 years and older or Lansky score equal or greater than 70% for patients less than 16 years old (See Appendix B; inpatient Leukemia service transfers without discharge are acceptable provided patient has equivalent KPS as if were outpatient). 6. Renal and Liver function: 1. Calculated creatinine clearance \> 50 ml/min. 2. Bilirubin \< 2 mg/dL (unless benign congenital hyperbilirubinemia or hemolysis). 3. ALT \< 5 x upper limit of normal (ULN). 7. Pulmonary function: Spirometry corrected DLCO ≥ 60% predicted. This criteria is waived for patients who are developmentally unable to complete pulmonary function test. 8. Left ventricular ejection fraction (MOD-bp) \> 50%. 9. Graft Criteria: 1. Two CB units will be selected according to the current MDACC CB unit selection algorithm. 2. High resolution 8-allele HLA typing and recipient HLA antibody profile will be performed. 3. Unit selection will occur based on HLA-match, total nucleated cell (TNC), and CD34+ cell dose adjusted per patient body weight. 4. The bank of origin will also be considered. 5. Donor-specific HLA antibodies, if present, will also be taken into consideration. 6. Each CB unit must be at least 3/8 HLA-matched to the patient considering high-resolution 8-allele HLA typing. 7. Each CB unit will be required to have a cryopreserved TNC dose of at least 1.5 x 107 TNC/ recipient body weight (TNC/ kg). 8. Each CB unit will be required to have a cryopreserved CD34+ cell dose of at least 1.0 x 105 CD34+ cells/ recipient body weight (CD34+ cells/kg). 9. A minimum of one unit will be reserved as a backup graft. 10. Each CB unit will be required to be cryopreserved in standard cryovolume. (24- 27 ml/s per unit) and be red blood cell depleted.