Inclusion Criteria:

• Have relapsed or refractory MM after at least one line of therapy
• Have a confirmed diagnosis of MM with measurable disease, as defined by the presence of monoclonal immunoglobulin protein in serum electrophoreses of at least 0.5 g/dL for immunoglobulin G (IgG) or 0.25 g/dL for IgA, or measurable light chain in serum (100 mg/L) or urinary excretion of at least 200 mg monoclonal light chain per 24 hours
• Have NO continuing acute toxic effects (except alopecia) of any prior chemotherapy, radiotherapy or surgical procedures; all such effects must have resolved to Common Terminology Criteria for Adverse Events (CTCAE, Version 4.03) grade =< 1; surgery (except minor procedures such as biopsies, IV line placement, etc.) must have occurred at least 28 days prior to study enrollment
• Have received NO anti-cancer therapy within 28 days prior to receiving study drug
• Have received NO radiotherapy within 14 days prior to receiving study drug
• Have an Eastern Cooperative Oncology Group (ECOG) Performance score =< 2
• Have a life expectancy of at least 3 months
• Absolute neutrophil count (ANC) >= 1 x 10^9 (International System [SI] units 10^9/L) (with or without filgrastim [G-CSF])
• Platelets >= 50 x10^9 (SI units 10^9/L)
• Serum creatinine =< 2 x upper limit of normal (ULN)
• Bilirubin =< 1.5 x ULN
• Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 3 x ULN (=< 5 x ULN if patients have liver involvement with MM)
• Proteinuria < grade 2
• Have a negative pregnancy test if a female with childbearing potential
• Have signed an informed consent indicating that the patient is aware of the neoplastic nature of their disease and have been informed of the procedures of the protocol, the experimental nature of the therapy, possible alternative therapies, potential benefits, side effects, risks, and discomforts
• Be willing and able to comply with scheduled visits, the treatment plan, and laboratory tests

Exclusion Criteria:

• Have a history of or current evidence of intracranial disease; patients with brain metastases must be excluded from this clinical trial
• Be on immunosuppressive therapy or have known human immunodeficiency virus (HIV) infection or active hepatitis B or C
• Be a pregnant or breast-feeding woman; female patients of childbearing potential must agree to use effective contraception, must be surgically sterile, or must be postmenopausal; male patients must agree to use effective contraception or be surgically sterile; barrier methods are a recommended form of contraception
• Have clinically significant cardiac disease (New York Heart Association, class III or IV) including pre-existing arrhythmia, uncontrolled angina pectoris, myocardial infarction 1 year prior to study entry, or a known history of grade 2 or higher compromised left ventricular ejection fraction
• Have dementia or altered mental status that would prohibit informed consent
• Have any other severe, acute or chronic medical or psychiatric condition or laboratory abnormality that may increase the risk associated with study participation or study drug administration or may interfere with the interpretation of study results and, in the judgment of the principal investigator, would make the patient inappropriate for this study
• Have a history of sensitivity to bortezomib, boron or mannitol
• Have grade 2 or greater neuropathy at the time of screening
• Have progressed while receiving a bortezomib-containing regimen; patients who develop progressive disease as per the International Working Group (IWG) criteria at least 3 months after their last dose of bortezomib are eligible