The purpose of this study is to evaluate the safety and efficacy of siltuximab in participants with relapsed (the return of a disease or the signs and symptoms of a disease after a period of improvement.) or refractory (cancer that does not respond to treatment) multiple myeloma (a type of cancer that begins in plasma cells [white blood cells that produce antibodies]).

This is an open-label (all people know the identity of the intervention), multicenter (when more than one hospital or medical school team work on a medical research study), non-randomized (a clinical trial in which the participants are not assigned by chance to different treatment groups), prospective (study following participants forward in time) safety and efficacy study of siltuximab in participants with relapsed or refractory multiple myeloma. The study consists of 3 Phases: Screening Phase (from first visit until the first dose of study drug), Treatment Phase (from the first dose to the end-of-treatment), and Follow-up Phase (after end-of-treatment until the end of study). The duration of participation in the study for an individual participant will be up to 4 weeks for Screening Phase, approximately 52 weeks for Treatment Phase and until death, lost to follow-up, withdraw of consent or end of study, whichever, comes first for Follow-up Phase. Treatment will be administered on a 28-day cycle. The study is designed with 2 alternative treatment plans. Treatment Plan A: during first 2 cycles siltuximab will be administered alone, dexamethasone may be added to the treatment regimen based on the participant's response to treatment. Treatment Plan B: siltuximab and dexamethasone combination for the duration of the study. The first 14 eligible participants will follow Treatment Plan A and data evaluation will be conducted for participants after 2 cycles of treatment and 2 post baseline disease assessments. If at least one complete response (CR) or partial response (PR) is observed in 14 participants, all subsequent participants will follow Treatment Plan A. However, if no responses (CR or PR) are observed, all subsequent participants will follow Treatment Plan B. The primary efficacy endpoint will be percentage of participants with overall response. Participants' safety will be monitored throughout the study.

Inclusion Criteria:

• Confirmed diagnosis of multiple myeloma with relapsed or refractory disease after failing at least 2 prior lines of therapy
• Prior treatment regimen must have included bortezomib (alone or in combination with other agents)
• Measurable secretory disease defined as either serum monoclonal paraprotein (M- protein) greater than or equal to (>=) 1 gram per deciliter (g/dL) or urine monoclonal (light chain) protein (greater than (>) 200 milligram/24 hours)
• Eastern Cooperative Oncology Group (ECOG) performance status score of less than or equal to (<=) 2 - Participants of childbearing potential must use adequate birth control measures, female participants of childbearing potential must have a negative serum pregnancy test at screening

Exclusion Criteria:

• Treatment with systemic cancer therapy (including clarithromycin) or radiotherapy within 30 days before the first dose of study agent - Treatment with nitrosoureas (a group of alkylating agents used as antineoplastic drugs in the chemotherapy) within 42 days before the first dose of study agent
• Major surgery within 30 days before the first dose of study agent or planning to have surgery (except for minor surgical procedures) during the study
• Serious concurrent illness (medical or psychiatric), uncontrolled infection, or significant cardiac disease characterized by significant ischemic coronary disease (an imbalance between myocardial functional requirements and the capacity of the coronary vessels to supply sufficient blood flow) or congestive heart failure (condition in which the heart is unable to pump out sufficient blood to meet the metabolic need of the body) not under medical control, or any uncontrolled medical condition (for example: uncontrolled diabetes), including the presence of clinical laboratory abnormalities, that places the subject at unacceptable risk by participating in the study or confounds the ability to interpret data from the study
• Known to be seropositive (giving a positive result in a test of blood serum) for Human Immunodeficiency Virus (HIV), or active hepatitis A, B or C infection