Brief Summary: This phase II trial studies how well tacrolimus, bortezomib, and anti-thymocyte globulin (thymoglobulin) work in preventing low toxicity graft versus host disease (GVHD) in patients with blood cancer who are undergoing donor stem cell transplant. Tacrolimus and anti-thymocyte globulin may reduce the risk of the recipient's body rejecting the transplant by suppressing the recipient's immune system. Giving bortezomib after the transplant may help prevent GVHD by stopping the donor's cells from attacking the recipient. Giving tacrolimus, bortezomib, and anti-thymocyte globulin may be a better way to prevent low toxicity GVHD in patients with blood cancer undergoing donor stem cell transplant.

Detailed Description: PRIMARY OBJECTIVES: I. To determine a composite end point of alive and severe acute GVHD free at 6 months following human leukocyte antigen (HLA) matched related or unrelated donor hematopoietic peripheral blood transplant in patients with hematologic malignancies who receive the immunosuppressive combination tacrolimus, bortezomib, anti-thymocyte globulin (TBT) as GVHD prophylaxis. II. To determine the safety of this combination in the first six months post-transplant. SECONDARY OBJECTIVES: I. To determine the cumulative incidence of grade III-IV aGVHD. II. To determine incidence and severity of chronic GVHD. III. To determine disease relapse or progression overall and disease free survival at one year. OUTLINE: Patients receive tacrolimus intravenously (IV) on day -3 through day 180. Patients may receive tacrolimus orally (PO) later at the doctor's discretion. Patients receive anti-thymocyte globulin IV on days -3, -2, and -1 and bortezomib IV on day 0 and day 3. Patients undergo allogeneic bone marrow transplant on day 0. After completion of study treatment, patients are followed up for 6 months and then periodically for up to 2 years.