The purpose of this study is to see what effects CNTO 328 has on relapsed or refractory multiple myeloma. The study drug, CNTO 328, is a chimeric (part mouse) antibody (small protein that is important for fighting infection).CNTO 328 blocks a small protein called Interleukin 6 (IL-6). IL-6 is made naturally by your body, and at normal levels is important for inflammatory response. High levels of IL-6 can help cancer cells grow and interfere with chemotherapy drugs killing cancer cells. Cancer-related sickness such as cachexia (weight loss), bone resorption (weakening of your bones), and depression have been linked to high levels of IL-6. CNTO 328 has been shown to slow down tumor growth or shrink tumors when tested in animals. In other clinical trials, over 100 patients have received CNTO 328. There are studies ongoing in participants with kidney cancer, hematologic malignancies (blood cancers such as multiple myeloma), and prostate cancer, to see if CNTO 328 is safe and to see what effects it has on these types of cancer. At this time, it is unknown what effect CNTO 328 has had on the participants' cancer. Bortezomib is a type of drug known as a "proteasome inhibitor." A proteasome is a substance that is found in every cell and it is there to help to break down other substances ('proteins') and has a role in the way cells divide. If the proteasome is inhibited, it cannot perform its function in the cell, and if a cell cannot divide it dies. Over 8000 patients with multiple myeloma and other types of cancer have been treated with bortezomib. Bortezomib has been extensively studied in patients with previously treated multiple myeloma. Based on its established activity in pretreated multiple myeloma, bortezomib is registered in the United States and in Europe for the treatment of multiple myeloma patients who have received at least two prior therapies and have demonstrated disease progression on the last therapy. Bortezomib is currently also being studied in several other cancer types.This study consists of two parts. The purpose of Part 1 is to determine the safety of CNTO 328 and bortezomib when given together as a treatment. The purpose of Part 2 is to compare the safety and effects (good and bad) of the combination of CNTO 328 and bortezomib to the safety and effects of bortezomib alone. About 20 patients will take part in the first part of the study. About 270 patients will take part in the second part of the study at approximately 70 sites in the US, Canada, and Europe. Patients will be in the study for about 12 months, with a follow-up period of around 9 months. The study is divided into four different phases: Screening phase-which lasts up to 4 weeks. During this phase the study doctor will perform tests to see if the patient can participate in the study.Treatment phase-which may last up to 4 cycles of 42 days each during which the patient will be treated with CNTO 328 and bortezomib. Maintenance phase-If the patient benefits from the therapy in the treatment phase, the patient will continue to receive CNTO 328 and bortezomib, but now in cycles of 35 days each. Follow up phase, this includes an end of treatment visit 4 weeks after the patient's last infusion and follow up visits every three months until the patient starts a new anti-cancer treatment. CNTO 328 6mg/kg ( 6 milligrams per kilogram of body weight) will be given intravenously (into the vein) over 2 hours once every 2 weeks. Patients who respond with stable disease or better may receive additional doses. Bortezomib will be given IV (into the vein) at 1.3 mg/m2 over 3-5 seconds twice a week for 2 weeks followed by 1 week of rest.