Inclusion Criteria

* Patient is of a legally 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performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to their future medical care.
* Female patient is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study.
* Male patient agrees to use an acceptable method for contraception for the duration of the study.
* Patient was previously diagnosed with multiple myeloma based on standard criteria and currently requires second-, third-, or fourth-line therapy because of PD, defined as a 25% increase in M-protein, development of new or worsening of existing lytic bone lesions or soft tissue plasmacytomas, or hypercalcemia (serum calcium \>11.5 mg/dL), or relapse from CR.
* Patient has measurable disease, defined as follows:
* For secretory multiple myeloma, measurable disease is defined as any quantifiable serum monoclonal protein value (generally, but not exclusively, greater than 1 g/dL of IgG M-Protein and greater than 0.5g/dL IgA) and, where applicable, urine light-chain excretion of ≥200 mg/24 hours.
* For oligo- or non-secretory multiple myeloma, measurable disease is defined by the presence of soft tissue (not bone) plasmacytomas as determined by clinical examination or applicable radiographs (i.e. MRI, CT-Scan). In patients with oligosecretory multiple myeloma, the serum and/or urine M-protein measurements are very low and difficult to follow for response assessments. Therefore, other disease sites (bone marrow; extramedullary mass) must be assessed and followed. In patients with non-secretory multiple myeloma, there is no M-protein in serum or urine by immunofixation.
* Patient has a Karnofsky performance status ≥60%.
* Patient has a life-expectancy \>3 months.
* Patient has the following laboratory values at and within 14 days before Baseline (Day 1 of Cycle 1, before study drug administration):
* Platelet count ≥50 x 10E+9/L without transfusion support within 7 days before the laboratory test.
* Hemoglobin ≥7.5 g/dL, without transfusion support within 7 days before the laboratory test.
* Absolute neutrophil count (ANC) ≥0.75 x 10E+9/L without the use of colony stimulating factors.
* Corrected serum calcium \<14 mg/dL (3.5 mmol/L).
* Aspartate transaminase (AST): ≤2.5 x the upper limit of normal (ULN).
* Alanine transaminase (ALT): ≤2.5 x the ULN.
* Total bilirubin: ≤1.5 x the ULN.
* Calculated or measured creatinine clearance: ≥20 mL/minute.

Exclusion Criteria

* Patient previously received treatment with VELCADE.
* Patient previously was refractory to treatment with high-dose dexamethasone, as experiencing less than a partial response to or PD within 6 months after discontinuing dexamethasone, or discontinued dexamethasone because of ≥Grade 3 dexamethasone-related toxicity.
* Previous high-dose dexamethasone therapy is defined as \>500 mg dexamethasone or equivalent over a 10-week period, whether administered alone or as part of the VAD regimen.
* Patient received nitrosoureas within 6 weeks or any other chemotherapy, including thalidomide or clarithromycin, or radiation therapy within 3 weeks before enrollment.
* Patient received corticosteroids (\>10 mg/day prednisone or equivalent) within 3 weeks before enrollment.
* Patient received immunotherapy or antibody therapy within 8 weeks before enrollment.
* Patient received plasmapheresis within 4 weeks before enrollment.
* Patient had major surgery within 4 weeks before enrollment. (Kyphoplasty is not considered major surgery.)
* Patient has a history of allergic reaction attributable to compounds containing boron or mannitol.
* Patient has peripheral neuropathy of Grade 2 or greater intensity, as defined by the NCI Common Toxicity Criteria (NCI CTC):
* Grade 2: Objective sensory loss or paresthesia (including tingling), interfering with function, but not interfering with activities of daily living (ADLs).
* Grade 3: Sensory loss or paresthesia interfering with ADLs.
* Grade 4: Permanent sensory loss that interferes with function.
* Patient had 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 electrocardiographic evidence of acute ischemia or active conduction system abnormalities.
* Patient was treated for a cancer other than multiple myeloma within 5 years before enrollment, with the exception of basal cell carcinoma or cervical cancer in situ.
* 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 according to this protocol.
* Patient is known to be human immunodeficiency virus (HIV)-positive. (Patients assessed by the investigator to be at risk for HIV infection should be tested in accordance with local regulations.)
* Patient is known to be hepatitis B surface antigen-positive or has known active hepatitis C infection.
* Patient has an active systemic infection requiring treatment.
* Female patient is pregnant or breast-feeding.
* Patient currently is enrolled in another clinical research study and/or is receiving an investigational agent for any reason.