This is a 2-part, open-label (all people know the identity of the intervention) multicenter (when more than 1 hospital or medical school team work on a medical research study), Phase 2 study to evaluate the safety and efficacy of the combination of siltuximab plus mitoxantrone versus mitoxantrone in participants with metastatic HRPC who have received 1 prior Docetaxel-based chemotherapy (treatment of disease, usually cancer, by chemical agents) regimen (pattern of giving treatment). Part 1 of the study is single arm where participants will receive mitoxantrone, prednisone and siltuximab. Part 2 of the study is randomized portion (the study drug is assigned by chance), consisting of 2-arms. The experimental arm will consist of treatment with mitoxantrone, prednisone and siltuximab. The control arm will consist of treatment with mitoxantrone and prednisone. Mitoxantrone will be administered at a dose of 12 milligram per square meter (mg/m^2) intravenously (into a vein) as a 30-minute infusion (a fluid or a medicine delivered into a vein by way of a needle) on Day 1 of each 3-week cycle, until disease progression or unacceptable toxicity (any harmful effect of a drug) or up to 10 cycles (a maximum total dose of approximately 120 mg/m^2). Siltuximab will be administered at a dose of 6 mg/kilogram intravenously as a 2-hour infusion, starting Day 1 of Cycle 1 to continue every 2 weeks until disease progression or unacceptable toxicity or up to a maximum of 1 year. All participants will receive prednisone 5 mg twice daily starting with the first administration of Mitoxantrone. The duration of treatment will be a maximum of 12 months for cumulative dose. Radiologic assessments will be performed on Week 12 after the first study agent dosing, then every 9 weeks until the end of treatment and then once every 3 months until documented disease progression. Tumor (a mass in a specific area) response will be assessed using Response Evaluation Criteria in Solid Tumors (RECIST) criteria. There will be short-term follow-up visits (conducted monthly for 2 months), followed by long-term follow-up visits (conducted once every 3 months). Participants' safety will also be monitored throughout the study.