Inclusion Criteria:

- History of histologically documented multiple myeloma with relapsed or resistant
disease, defined as previously treated with/without autologous stem cell
transplantation and is either relapsing or is resistant after > 1 line of prior
therapy for myeloma

- Patients can not be eligible for MTRC phase III protocols of higher priority

- Performance status of greater than or equal to 2 as per SWOG scale

- Patients must have an absolute neutrophil count > 750/mm3, and a platelet count
greater than or equal to 25,000/mm3

- No prior malignancy is allowed except for adequately treated basal cell or squamous
cell skin cancer, in situ cervical cancer, or other cancer for which the patient has
been disease free for at least three years. Prior malignancy is acceptable provided
there has been no evidence of disease within the three-year interval

- Pregnant or nursing women may not participate. Women of childbearing potential must
have a negative pregnancy documented within one week of registration. Women/men of
reproductive potential may not participate unless they have agreed to use an
effective contraceptive method.

- Male or female adults of at least 18 years of age.

- Signed written informed consent and willingness to meet follow-up schedule and study
procedure obligations

Exclusion Criteria:

- Chemotherapy or radiotherapy received within the previous 2 weeks

- Prior Treatment of PS-341

- Significant neurotoxicity, defined as grade greater than or equal to 2 neurotoxicity
per NCI Common Toxicity Criteria

- POEMS Syndrome

- Non-secretory multiple myeloma

- Active infection requiring antibiotics

- Clinically significant hepatic dysfunction in the absence of liver metastases as
noted by bilirubin or AST >3 times the upper normal limit or clinically significant
concurrent hepatitis

- New York Hospital Association (NYHA) Class III or Class IV heart failure

- Myocardial infarction within the last 6 months

- Poorly controlled hypertension, diabetes mellitus, or other serious or psychiatric
illness that could potentially interfere with the completion of treatment according
to this protocol

- Severe renal dysfunction defined as a creatinine clearance < 20 cc/min.

- Absolute neutrophil count < 750/mm3, and a platelet count < 25,000/mm3

- Pregnant or potential for pregnancy

- Breast-feeding