This is an Open-Label (all people know the identity of the intervention), non-randomized, multicenter (when more than one hospital or medical school team work on a medical research study), single arm study to evaluate the safety and efficacy of bortezomib in participants with multiple myeloma (cancer of the types of cells normally found in bone marrow) who have previously responded to a bortezomib based therapy. Participants will be non-randomly assigned to single group bortezomib. Participants will be treated with bortezomib alone or in combination with another drug (dexamethasone). Bortezomib will be given intravenously (i.v. [into a vein]) twice Weekly, on Days 1, 4, 8 and 11 of each cycle followed by a 10-day (Days 12 to 21) rest period. The total duration of treatment period will be 8 cycles, each lasting 3 weeks. The initial bortezomib dose is the last tolerated dose (1.0 or 1.3 milligram per metersquare [mg/ m^2] on the previous bortezomib-based treatment. Participants who start the study on a dose of 1.0 mg/m^2 bortezomib and tolerate the dose well could have their dose escalated to 1.3 mg/m^2. Doses above 1.3 mg/m^2 are not allowed. A complete cycle comprises 4 doses of bortezomib. Dexamethasone will be first introduced in Cycles 1 to 5 (i.e.dexamethasone will not be introduced for the first time in Cycles 6 to 8). The median total dose of dexamethasone received per cycle ranges from 120 mg (cycle 7) to 160 mg (cycles 1 to 6 and 8). Efficacy will be primarily assessed by determining Best Confirmed Response according to the European Group for Blood and Marrow Transplantation (EBMT) criteria. Participant's safety will be monitored throughout the study.