Donor Umbilical Cord Blood Natural Killer Cells, Aldesleukin and Umbilical Cord Blood Transplant in Patients With Refractory Hematologic Cancers.

OBJECTIVES: Primary * Determine the incidence of 6-month disease free survival. The primary laboratory objective is the measure of in vivo expansion of umbilical cord blood (UCB) derived natural killer cells (NK) after a fully ablative preparative regimen. Secondary * Determine the incidence of transplant-related mortality at 6 months after NK UCB + double UCBT * Evaluate the pattern of chimerism after NK UCB + double UCBT * Determine the incidence of neutrophil engraftment at day 42 after NK UCB + double umbilical cord blood transplantation (UCBT) * Determine the incidence of platelet engraftment at 6 months after NK UCB + double UCBT * Determine the incidence of acute graft-versus-host disease (GVHD) grade II-IV and grade III-IV at day 100 after NK UCB + double UCBT * Determine the incidence of chronic GVHD at 1 year after NK UCB + double UCBT * Determine the disease-free survival at 1 after NK UCB + double UCBT * Determine the incidence of relapse at 1 after NK UCB + double UCBT OUTLINE: This is a single arm, nonrandomized, open-label study. * Myeloablative conditioning regimen: Patients receive fludarabine intravenously (IV) over 1 hour on days -18 to -16 and cyclophosphamide intravenously (IV) on days -18 and -17. Patients undergo total-body irradiation twice daily on days -16 to -13. * Haploidentical umbilical cord blood (UCB) natural killer (NK) cell therapy and aldesleukin: Patients undergo haploidentical UCB-enriched NK cell (CD3- depleted) infusion on day -13. Patients then receive aldesleukin subcutaneously on days -13, -11, -9, -7, -5, and -3. Some patients may also receive methylprednisolone IV on days -1 and 0. * UCB transplantation (UCBT): Patients undergo a single or double UCBT on day 0. Beginning on day 1, patients receive filgrastim (G-CSF) IV once daily until blood counts recover. * Graft-vs-host disease (GVHD) prophylaxis: Patients receive cyclosporine IV over 2 hours 2-3 times daily beginning on day -1 and continuing until day 100, followed by a taper until day 180. Patients also receive mycophenolate mofetil IV or orally 2-3 times daily beginning on day -1 and continuing until day 30 (or 7 days after engraftment) in the absence of acute GVHD.