A Study of PS-341 Given to Patients With Multiple Myeloma Who Experienced Progressive Disease After Receiving Dexamethasone in M34101-039

Inclusion Criteria * Patient experienced PD, as defined by SWOG+ criteria during or after treatment with high-dose dexamethasone in MPI Study M34101-039, but has not received alternate anti-neoplastic therapy. Intolerance to high-dose dexamethasone therapy as administered in MPI study M34101-039 does not qualify as PD. * Patient is, in the investigator's opinion, willing and able to comply with the protocol requirements. * Patient has given voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to their future medical care. * Female patient is post-menopausal, surgically sterilized, or willing to use acceptable methods of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) from Screening through the End of Treatment visit. * Male patient agrees to use an acceptable barrier method for contraception from Screening through the End of Treatment visit. * Patient meets the following pretreatment laboratory criteria at and within 14 days before Baseline (Day 1 of Cycle 1, before study drug administration). (Note that the End of Treatment assessments of MPI study M34101-039 may qualify as the Screening assessments for MPI study M34101-040 if performed within 14 days of the Baseline visit.): * Platelet count ≥20 X 10E+9/L, with or without transfusion support. * Hemoglobin ≥7.0 g/dL, with or without transfusion support. * Absolute neutrophil count (ANC)≥0.5 x 10E+9/L, without growth factor support. * Serum calcium \<14 mg/dL (3.5 mmol/L). * Aspartate transaminase (AST):≤2.5 x the upper limit of normal (ULN). * Alanine transaminase (ALT):≤2.5 x the ULN. * Total bilirubin:≤1.5 x the ULN. * If calculated or measured creatinine clearance: ≥20 mL/minute, assessments are as specified in the protocol. If calculated or measured creatinine clearance is \<20 mL/minute. Exclusion Criteria * Patient participated in M34101-039 and did not have confirmed PD. Dexamethasone intolerance does not qualify as PD. * Patient had PD on the dexamethasone arm of the MPI Study M34101-039, and then received alternate anti-neoplastic therapy. * Patient has not recovered from dexamethasone-related toxicity experienced during MPI Study M34101-039. * Patient is known to be human immunodeficiency virus (HIV)-positive.(Patients assessed by the investigator to be at risk for HIV infection should be tested in accordance with local regulations.) * Patient is known to be hepatitis B surface antigen-positive or has known active hepatitis C infection.(Patients assessed by the investigator to be at risk for hepatitis B or C infection should be tested in accordance with local regulations.) * Female patient is pregnant or breast-feeding. * Patient developed a new or experienced worsening of an existing illness during or after completion of Study M34101-039 that, in the investigator's opinion, may put the patient at risk of participation in this study.