Inclusion Criteria:

- Diagnosis of multiple myeloma (MM)

- Salmon-Durie stage IIA or IIIA OR progressive stage IA disease

- Meets at least 1 major AND 1 minor criterion OR at least 3 minor criteria

- The following are considered major criteria:

- Plasmacytoma on tissue biopsy

- Bone marrow plasmacytosis with >= 30% plasma cells

- Monoclonal globulin spike on serum protein electrophoresis exceeding 3.5
g/dL for immunoglobulin (Ig) G peaks or 2.0 g/dL for IgA peaks OR the
presence of Bence-Jones protein of >= 1 g/24 hour-urine collection

- The following are considered minor criteria:

- Bone marrow plasmacytosis 10-29%

- Monoclonal globulin spike present, but less than the levels defined for a
major criterion

- Lytic bone lesion

- Decrease in normal IgM < 50 mg/dL, IgA < 100 mg/dL, or IgG < 600 mg/dL

- No non-secretory MM (absent serum or urinary M-protein)

- Failed at least 1 prior systemic therapy* (e.g., chemotherapy, high-dose
corticosteroids, thalidomide, or bortezomib) for the treatment of MM

- No solitary plasmacytoma

- Performance status - ECOG 0-2

- More than 6 months

- Absolute neutrophil count > 1,200/mm^3

- Platelet count > 75,000/mm^3

- AST and ALT =< 2.5 times upper limit of normal (ULN)

- Bilirubin =< 1.5 times ULN

- Creatinine =< 1.5 times ULN

- No symptomatic congestive heart failure

- No unstable angina pectoris

- No cardiac arrhythmia

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception

- Fasting cholesterol =< 350 mg/dL

- Triglycerides =< 400 mg/dL

- No other concurrent uncontrolled illness

- No active or ongoing infection requiring oral or IV antibiotics

- No prior allergic reaction to compounds of similar chemical or biological composition
to CCI-779

- No other prior or concurrent malignancy or myelodysplasia except for the following:

- Basal cell or squamous cell skin cancer

- Carcinoma in situ of the cervix

- Localized cancer treated with surgery only with no evidence of disease for > 5
years

- No psychiatric illness or social situation that would preclude study compliance

- More than 4 weeks since prior thalidomide and recovered

- Prior high-dose chemotherapy and stem cell transplantation allowed

- More than 4 weeks since prior chemotherapy and recovered

- More than 4 weeks since prior high-dose corticosteroids and recovered

- More than 4 weeks since prior bortezomib and recovered

- More than 4 weeks since other prior anti-myeloma systemic therapy and recovered

- No concurrent combination antiretroviral therapy for HIV-positive patients

- No other concurrent investigational agents

- No other concurrent anticancer therapy