Tacrolimus, Bortezomib, & Thymoglobulin in Preventing Low Toxicity GVHD in Donor Blood Stem Cell Transplant Patients

Inclusion Criteria: * Patients with acute leukemia, chronic myelogenous leukemia, myeloproliferative disorder and myelodysplasia with no circulating blasts and with less than 5% blasts in the bone marrow within 4 weeks of the start of transplant conditioning regimen * Patients with chronic lymphocytic leukemia/small lymphocytic lymphoma; follicular, marginal zone, diffuse large B-cell or mantle cell lymphoma with chemo-sensitive disease at time of transplant * Patients must have a related or unrelated peripheral blood stem cell donor; sibling donor must be a 6/6 match for human leukocyte antigen (HLA)-A and -B at intermediate (or higher) resolution, and -DRB1 at high resolution using deoxyribonucleic acid (DNA)-based typing, and must be willing to donate peripheral blood stem cells and meet institutional criteria for donation; unrelated donor must be 8/8 match at HLA-A, -B, -C and -DRB1 at high resolution using DNA-based typing; unrelated donor must be willing to donate peripheral blood stem cells and be medically eligible to donate stem cells according to National Marrow Donor Program (NMDP) criteria * Cardiac function: ejection fraction \> 40% * Estimated creatinine clearance greater than 50 mL/minute (using the Cockcroft-Gault formula and actual body weight) * Pulmonary function: carbon monoxide diffusing capability test (DLCO) ≥ 40% (adjusted for hemoglobin) and forced expiratory volume in 1 second (FEV1) ≥ 50% * Total bilirubin \< 1.5 x the upper limit of normal; patients who have been diagnosed with Gilbert's disease are allowed to exceed the defined bilirubin value of 1.5 x the upper limit of normal * Alanine aminotransferase (ALT)/aspartate aminotransferase (AST) \< 2.5 x the upper normal limit * Female subjects (unless postmenopausal for at least 1 year before the screening visit, or surgically sterilized), agree to practice two effective methods of contraception or agree to completely abstain from heterosexual intercourse from the time of signing the informed consent through 12 months post-transplant * Male subjects (even if surgically sterilized), of partners of women of childbearing potential must agree to practice effective barrier contraception or abstain from heterosexual intercourse from the time of signing the informed consent through 12 months post-transplant * Signed informed consent Exclusion Criteria: * Prior allogeneic transplant * Karnofsky performance score \< 70% * Active central nervous system (CNS) involvement by malignant cells * Patients with uncontrolled bacterial, viral, or fungal infections (currently taking medication and with progression or no clinical improvement) at time of enrollment * Patients with transformed lymphoma (e.g., Richter's transformation arising in follicular lymphoma or chronic lymphocytic leukemia) * Patients seropositive for the human immunodeficiency virus (HIV) * Patient with active hepatitis B or C * Patients with hypersensitivity to bortezomib, boron, or mannitol * Patients with \> grade 2 sensory peripheral neuropathy * Myocardial infarction within 6 months prior to enrollment or New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities; prior to study entry, any electrocardiography (ECG) abnormality at screening must be documented by the investigator as not medically relevant * Female patients who are lactating or pregnant * Patients with a serious medical or psychiatric illness likely to interfere with participation in this clinical study * Patients with prior malignancies, except resected basal cell carcinoma or treated cervical carcinoma in situ; cancer treated with curative intent \> 5 years previously will be allowed; cancer treated with curative intent \< 5 years previously will not be allowed unless approved by the protocol officer or one of the protocol chairs