Reduced Intensity Allogeneic HCT in Advanced Hematologic Malignancies w/T-Cell Depleted Graft

The objectives for the study are listed below: Primary Objectives \*Determine the safety, and feasibility of administration of several dose combinations of conventional T-cells (Tcon) and regulatory T-cells (Treg) in subjects undergoing allogeneic hematopoietic cell transplantation (HCT) with related/unrelated HLA-matched or mismatched donors, or haploidentical donors with reduced intensity conditioning preparative regimen. Secondary Objectives * To determine the GVHD-free relapse-free survival (GRFS) post-HCT * To determine the overall survival (OS) post-HCT * To measure the incidence and severity of acute and chronic GVHD Exploratory Objectives * To measure the incidence of serious infections * To measure the incidence and timing of engraftment * To measure T cell immunity reconstitution parameters