Combination CCI-779 (Temsirolimus) and Bortezomib (Velcade) in Relapsed and/or Relapsed/Refractory Multiple Myeloma

Inclusion Criteria:

* 18 years of age or older
* Must have received prior therapy for their myeloma and have relapsed and/or relapsed/refractory multiple myeloma
* Monoclonal protein in the serum of greater than or equal to 1 gm/dL or monoclonal light chain in the urine protein electrophoresis of greater than or equal to 200mg/24 hours, or measurable light chains by free light chain assay of greater than or equal to 10mg/dl, or measurable plasmacytoma
* ECOG Performance Status 0, 1 or 2
* Laboratory values as outlined in the protocol

Exclusion Criteria:

* Uncontrolled infection
* Cytotoxic chemotherapy less than 2 weeks, or biologic therapy less than 2 weeks, or corticosteroids less than 2 weeks prior to registration. Patients may be receiving chronic corticosteroids if they are being given for disorders other than myeloma.
* Pregnant or nursing women
* Men or women of childbearing potential who are unwilling to employ adequate contraception
* Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy considered investigational within 14 days before enrollment
* Known to be HIV positive
* Myocardial infarction within 6 months prior to enrollment or has NYHA Class III or IV hear failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities
* Hypersensitivity to bortezomib, boron or mannitol
* Serious medical or psychiatric illness likely to interfere with participation in this clinical trial
* Patients who may need or are receiving live vaccines for immunization