This is a research study with an experimental drug called siltuximab (also known as CNTO 328). Siltuximab is being developed to see if it may be useful in treating multiple myeloma, including multiple myeloma that has returned after (relapsed) or did not respond (refractory) to previous treatment. Multiple myeloma is a type of cancer that affects the blood and bone marrow. The cancer cells in the bone marrow can cause the normal bone marrow cells to breakdown. This can result in low levels of red blood cells (which may make the patient feel tired or fatigued), low levels of white blood cells (which may increase the patient's chances of infections) or low levels of platelets (which may increase risk of bleeding). The cancer cells can cause damage to the normal bone. This can cause bone pain, bone fractures, and can increase the level of calcium in the blood. The cancer cells also make proteins (called M-proteins), which can result in damage to other organs, especially the kidneys. Siltuximab is a chimeric (part mouse and part human) antibody (immunoglobulin that is important for fighting infection). Siltuximab blocks another small protein called Interleukin 6 (IL-6). The body makes IL-6 naturally, and at normal levels it is important for the inflammatory response. But high levels of IL-6 can help cancer cells grow and interfere with chemotherapy drugs killing cancer cells. Cancer-related sicknesses such as weight loss, bone weakening, and depression have been linked to high levels of IL-6. This study tests the effectiveness and safety of siltuximab when it is taken together with Velcade and dexamethasone. There are two treatment groups, Arm A and Arm B. To try to make sure the groups are similar, patients will be put into Arm A or Arm B, randomly (by chance), like flipping a coin. Patients in Arm A will receive siltuximab plus Velcade and dexamethasone. Patients in Arm B will receive placebo plus Velcade and dexamethasone. About 500 patients will participate in the study. Velcade, also known as bortezomib, is injected directly into the vein all at once. This is called an intravenous (IV) push. Siltuximab or placebo is given as a 1 hour IV infusion through a small tube that goes directly into the vein. Dexamethasone is given orally. The treatment period is divided into cycles lasting about 21 days which will last until the patient's multiple myeloma gets worse, side effects that are not acceptable happen or when the patient decides to withdraw consent for treatment, whichever occurs first. Siltuximab 11mg/kg or placebo will be given on Day 1 of every cycle. Velcade 1.3 mg/m2 will be given on Days 1, 4, 8 and 11 for Cycles 1-8, and on Days 1 and 8 for Cycles 9 and higher. Dexamethasone 20 mg will be given on the day of and the day after each Velcade dose. Safety assessments will be performed throughout the study and include obtaining and evaluating laboratory tests, vital signs (e.g. blood pressure), and checking the occurrence and severity of adverse events. Disease assessments will also be performed and include obtaining and evaluating blood and 24 hour urine samples, bone marrow aspirate and/or biopsy samples and clinical and radiologic evaluations. After treatment, patients will enter the follow-up period, which includes visits up to 12 weeks after the last dose and checks every three months until death or the end of the study. Patients who stop treatment before their multiple myeloma gets worse will have disease assessments until their disease gets worse, they start a new multiple myeloma treatment, they decide to withdraw consent for study participation or the end of the study, whichever happens first. Siltuximab or placebo plus Velcade and dexamethasone will be given in 21-day treatment cycles until worsening of disease (progression), unacceptable toxicity or withdrawal of consent for treatment, whichever comes first. Siltuximab 11 mg/kg or placebo will be given on Day 1 of every cycle. Velcade 1.3 mg/m2 will be given on Days 1, 4, 8 and 11 for Cycles 1-8, and on Days 1 and 8 for Cycles 9 and higher. Dexamethasone 20 mg will be given on the day of and the day after each Velcade dose.