For these reasons, a primary focus for researchers is to engineer the graft to provide a T cell dose that will reduce the risk for GVHD, yet provide a sufficient number of cells to facilitate immune reconstitution and graft integrity. Building on prior institutional trials, this study will provide patients with a haploidentical graft engineered to specific T cell target values using the CliniMACS system. A reduced intensity, preparative regimen will be used in an effort to reduce regimen-related toxicity and mortality.