Bortezomib in Patients With Chronic Graft Versus Host Disease

Inclusion Criteria: * Voluntary written informed consent * Female subject is either postmenopausal for at least 1 year before the screening visit, is surgically sterilized or if they are of childbearing potential, agree to practice 2 effective methods of contraception from the time of signing the informed consent form through 30 days after the last dose of bortezomib, or agree to completely abstain from heterosexual intercourse. * Male subjects, even if surgically sterilized must agree to 2 effective methods of contraception. * Patients with chronic GVHD that involves 3 or more organs or with a score of 2 or greater in any single organ based on NIH cGVHD grading * Any previous treatments for cGVHD (except study drug). Participants may have received study drug for other reasons besides cGVHD such as leukemia or solid tumor. * Except for steroid refractory or intolerant cases, participants must be receiving baseline systemic glucocorticoid therapy for cGVHD at study entry. The dose of steroids must be stable for 14 days prior to starting study drug. * At the time of trial enrollment, participants may be receiving one or two other immunosuppressive therapies in addition to glucocorticoids. * Chronic GVHD manifestations that can be followed on physical or laboratory exam. * Age \>18 years old * ECOG performance status \< 2. Patients with ECOG performance status of 3 (defined as being capable of only limited self-care, confined to bed or chair more than 50% of waking hours) will also be eligible only if the lower performance status is judged to be directly related to steroid and/or cGVHD effects. * Myeloablative or non-myeloablative allogeneic hematopoietic cell transplant. Exclusion Criteria: * Patients with irreversible damage as the only manifestation of chronic GVHD (irreversible contractures or sicca syndrome) * Active uncontrolled infection * Contraindications to administration of bortezomib * Relapsed disease or development of other malignancies * Laboratory parameters: ANC \<1 x 10\^9/L Platelets \< 50 x 10\^9/L Bilirubin \>1.5 upper limit of normal (ULN) when it is clearly not related to GVHD. EF \<45% DLCO \<45% Creatinine clearance \<30 Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \> 5 × ULN * Platelet count of \<50 within 5 days before enrollment. * Absolute neutrophil count of \<1000 within 5 days before enrollment. * Patient has \> Grade 2 peripheral neuropathy * Patient had myocardial infarction within 6 months prior to enrollment or has 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 ECG abnormality at screening must be documented by the investigator as not medically relevant. * Patient has hypersensitivity to bortezomib, boron, or mannitol. * Female subject is pregnant or lactating. * Female patients who are lactating or have a positive serum pregnancy test during the screening period, or a positive urine pregnancy test on Day 1 before first dose of study drug, if applicable. * Serious medical or psychiatric illness likely to interfere with participation in this clinical study. * Diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy. * Participation in clinical trials with other investigational agents not included in this trial, within 14 days of the start of this trial and throughout the duration of this trial. * Radiation therapy within 3 weeks before randomization. Enrollment of subjects who require concurrent radiotherapy (which must be localized in its field size) should be deferred until the radiotherapy is completed and 3 weeks have elapsed since the last date of therapy.