The purpose of the first phase of the study is to determine whether, and at what dose, depsipeptide, bortezomib and dexamethasone can be safely administered to patients with Multiple Myeloma. The second phase of the study will establish whether depsipeptide, bortezomib and dexamethasone is effective in the treatment of patients with multiple myeloma. The study will also examine the role of maintenance therapy with depsipeptide.