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

The purpose of this research study is to determine the safety of CCI-779 (Temsirolimus) and bortezomib (Velcade), and the highest dose of this drug that can be given to people safely. We will also be looking at how the combination of the two drugs may work against multiple myeloma. CCI-779 (Temsirolimus) is a drug that appears to stop myeloma cells from growing.

* Since we are looking for the highest dose of CCI-779 (Temsirolimus) given in combination with bortezomib (Velcade) that can be given to people without causing the most serious or unmanageable side effects, not everyone who participates in this study will be receiving the same amount of either drug.
* During the study treatment, participants will be given some medications to decrease the chance they they will have an allergic reaction to CCI-779 (Temsirolimus). After these drugs are given, participants will be receive bortezomib (Velcade) by injection followed by an injection of CCI-779 (Temsirolimus). These drugs wil be given once a week for four weeks (on Days 1, 8, 15, and 22). On the fifth week (Day 29), participants will be given only CCI-779 along with the drugs to decrease the chance of an allergic reaction.
* The cycle will last 35 days and will occur twice before the doctor evaluates for response. The cycles will be repeated for up to 8 cycles as long as the participant does not have any severe or unmanageable side effects and the disease is responding to treatment.
* While receiving study treatment, participants will be seen at the clinic at the start of each cycle for the following: complete physical examination, blood work, urine collection, x-ray of bones (if study doctor deems necessary) and an electrocardiogram (prior to treatment and at the end of treatment)
* A bone skeletal survey will be performed at the end of treatment to measure the size of the participants tumors.
* After 8 cycles of treatment or if the participant has ended treatment, more tests will be performed. A physical exam, blood work, urine collection, skeletal survey, electrocardiogram, bone marrow biopsy and aspirate will be performed.

Eligibility Criteria:
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