Inclusion Criteria:

Major Criteria:

• Plasmacytomas on tissue biopsy
• Bone marrow plasmacytosis (> 30% plasma cells)
• Monoclonal IgG is > 3.5 g/dL or IgA is > 2.0 g/dL; kappa or lambda light chain excretion is > 1 g/day on a 24 hour urine sample.

Minor criteria:

• Bone marrow plasmacytosis (10 to 30%)
• Monoclonal immunoglobulin present but of lesser magnitude than given under major criteria.
• Lytic bone lesions

Other Eligibility Requirements:

• Patient is not eligible for Millennium Study M34101-039.
• Patient has received 4 or more lines of therapy for multiple myeloma and, in the investigator's opinion, currently needs therapy because of relapsed or progressive disease.
• Patient is of legal consenting age, as defined by local regulations.
• Patient is, in the investigator's opinion, willing and able to comply with the protocol requirements.
• Patient has given voluntary written informed consent before performance of any study-related procedure not part of normal medical care.
• Female patients must be either post-menopausal, surgically sterilized, or willing to use an acceptable method of birth control throughout the study.
• Male patients must agree to use an acceptable method of birth control throughout the study.
• Patient has a Karnofsky performance status of greater than or equal to 60%.
• Patient meets pretreatment laboratory criteria at and within 14 to 21 days before Baseline (Day 1 of Cycle 1, before study drug administration).

Exclusion Criteria:

• Patient progressed while receiving VELCADE previously in a clinical trial.
• Patient has been treated in Millennium Study M34101-039.
• Patient received corticosteroids (> 10 mg/day prednisone or equivalent) within 1 week before enrollment in the study.
• Patient received nitrosoureas within 6 weeks or any other chemotherapy within 3 weeks before enrollment in the study.
• Patient received immunotherapy or antibody therapy within 4 weeks before enrollment.
• Patient had major surgery with 4 weeks before enrollment (kyphoplasty isn't considered major surgery).
• Patient has a history of allergic reactions due to compounds containing boron or mannitol.
• Patient has peripheral neuropathy of Grade 2 or greater, as defined by the National Cancer Institute Common Toxicity Criteria (NCI CTC).
• Patient has a myocardial infarction within 6 months of enrollment or has New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias or electrocardiogram shows evidence of acute ischemia or active conduction system abnormalities.
• Patient has cardiac amyloidosis
• Patient has poorly controlled hypertension, diabetes mellitus, or other serious medical or psychiatric illness that could potentially interfere with the completion of treatment.
• Patient is known to be infected with human immunodeficiency virus (HIV positive).
• Patient is known to be hepatitis B positive or has active hepatitis C infection.
• Patient has an active systemic infection requiring treatment.
• Female patient is pregnant or breast-feeding. Confirmation that the patient is not pregnant is required. Pregnancy testing is not required for post-menopausal or surgically sterilized patients.