T-Regulatory Cell and CD3 Depleted Double Umbilical Cord Blood Transplantation in Hematologic Malignancies

Based on prior studies, the first patient will start at lowest dose combination (3 x 10\^6/kg of Treg and 3 x 10\^6/kg of CD3+ Teff cells). One patient will be entered at each level with a minimum of 35 days to observe the patient prior to moving to the next dose level. (1) If GVHD does not occur, a "successful step", then the CD3+ Teff cell dose will increase to the next higher level for the next patient; (2) If GVHD occurs, a "failed step", then Treg dose will increase to the next higher level for the next patient. It would take a minimum of 5 (if no GVHD) and maximum of 9 patients (if GVHD is observed at each level) to complete all Treg:CD3+ Teff cell combinations. An additional 10 patients will be enrolled to verify that this reflects the optimal combination and evaluate its safety profile.