This randomized phase II trial includes a blood stem cell transplant from an unrelated donor to treat blood cancer. The treatment also includes chemotherapy drugs, but in lower doses than conventional (standard) stem cell transplants. The researchers will compare two different drug combinations used to reduce the risk of a common but serious complication called "graft versus host disease" (GVHD) following the transplant. Two drugs, cyclosporine (CSP) and sirolimus (SIR), will be combined with either mycophenolate mofetil (MMF) or post-transplant cyclophosphamide (PTCy). This part of the transplant procedure is the main research focus of the study.