 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 participants 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. 