Phase 2/3 combination study comparing bortezomib plus one of three doses of tanespimycin in patients with relapsed-refractory multiple myeloma after failure of at least three prior anti-cancer therapy regimens. Prior therapy must include bortezomib and lenalidomide. Primary objective is to assess the dose-response relationship of objective response rate (ORR) using EBMT/IBMTR criteria of any three dose levels of tanespimycin (KOS-953) in combination with bortezomib after four treatment cycles.