Calcineurin Inhibitor-Free GVHD Prevention Regimen After Related Haplo PBSCT

The purpose of this study is to find out if a combination of drugs (these are called: cyclophosphamide, sirolimus, and mycophenolate mofetil) will protect participants better against graft vs. host disease (GVHD) after receiving a hematopoietic cell transplant from a related partially matched (haploidentical) donor. As part of the treatment for their blood cancer, participants need a hematopoietic cell transplantation (HCT) to improve their chances of cure. In any HCT, after the stem cell infusion is given, a combination of drugs is needed to prevent GVHD and facilitate acceptance of the graft.