Brief Summary: This phase II trial studies the side effects and best dose of bortezomib when given with chemotherapy and to see how well they work in treating participants with lymphoid malignancies undergoing stem cell transplant. Giving chemotherapy before a stem cell transplant helps stop the growth of cells in the bone marrow, including normal blood-forming cells (stem cells) and cancer cells. When the healthy stem cells from a donor are infused into the participant they may help the participant's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells called graft versus host disease. Giving tacrolimus and methotrexate after the transplant may stop this from happening. Giving bortezomib and chemotherapy may work better in treating participants with lymphoid malignancies undergoing a stem cell transplant.

Detailed Description: PRIMARY OBJECTIVES: I. To determine the maximum tolerated dose (MTD) and dose limiting toxicity (DLT) of Velcade (bortezomib) in patients with lymphoid malignancies undergoing allogeneic peripheral blood stem cell or bone marrow transplantation. II. To determine the 1-year disease-free-survival (DFS) and the toxicity profile of Velcade (bortezomib) in patients with lymphoid malignancies undergoing allogeneic peripheral blood stem cell or bone marrow transplantation. SECONDARY OBJECTIVES: I. To compare the incidence of graft versus host disease (GVHD) with historical controls. OUTLINE: This is a dose-escalation study of bortezomib. Participants receive carmustine intravenously (IV) over 1 hour on day -6, cytarabine IV over 1 hour twice daily (BID) on days -5 to -2, etoposide IV over 3 hours BID on days -5 to -2, and melphalan IV over 30 minutes on day -1. Participants also receive rituximab IV on days -13, -6, +1, and +8, and bortezomib IV over 1 minute on days -13, -6, -1, and +2. Participants receiving a matched unrelated or mismatched donor transplant also receive anti-thymocyte globulin IV over 4-6 hours on days -6 and -5. Participants then undergo allogeneic hematopoietic stem cell transplantation over 30-45 minutes on day 0 and receive filgrastim subcutaneously (SC) once daily (QD) starting on day +7 until blood counts return to normal level. Participants receive tacrolimus IV starting on day -2 changing to orally (PO) before leaving the hospital for 6-8 months after the transplant. Participants also receive methotrexate IV over a few minutes on days +1, +3, and +6 and those receiving a matched unrelated or mismatched donor transplant also receive methotrexate IV on day +11. After completion of study treatment, participants are followed up at 1 month, every 3 months for 1 year, and then every 6 months for 5 years.