Lenalidomide and Temsirolimus in Treating Patients With Previously Treated Multiple Myeloma

Inclusion Criteria: * Diagnosis of multiple myeloma (MM) * Salmon-Durie stage IIA or IIIA * No stage B disease * Meets ≥ 1 major AND 1 minor criterion OR ≥ 3 minor criteria * The following are considered major criteria: * Plasmacytoma on tissue biopsy * Bone marrow plasmacytosis with ≥ 30% plasma cells * Monoclonal paraprotein ≥ 3,500 mg/dL (IgG) or ≥ 2,000 mg/dL (IgA) OR monoclonal protein (Bence-Jones protein) ≥ 1,000 mg by 24-hour urine collection * The following are considered minor criteria: * Bone marrow plasmacytosis 10-29% of marrow cellularity * Monoclonal globulin spike \< 3,500 mg/dL (IgG) or \< 2,000 mg/dL (IgA) * Lytic bone lesions * Decrease in normal IgM (\< 50 mg/dL), IgA (\< 100 mg/dL), or IgG (\< 600 mg/dL) * Disease progression after ≥ 1 prior systemic treatment regimen\* for MM (e.g., chemotherapy, high-dose corticosteroids, thalidomide, or bortezomib), defined as \> 25% increase in serum or urine M-protein * No solitary plasmacytoma * No non-secretory MM (absent serum or urinary M-protein) * ECOG performance status 0-2 * Life expectancy \> 6 months * Bilirubin ≤ 1.5 times upper limit of normal (ULN) * AST and ALT ≤ 3 times ULN * Creatinine ≤ 2.0 mg/dL * Absolute neutrophil count ≥ 1,500/mm³ * Platelet count ≥ 100,000/mm³ * Fasting cholesterol ≤ 350 mg/dL * Fasting triglycerides ≤ 400 mg/dL * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective double-method contraception * Must agree not to donate blood, sperm, or ova during and for 4 weeks after completion of study treatment * 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 history of recurrent deep vein thrombosis (DVT)/pulmonary embolism (PE) or DVT/PE occurring while on therapeutic levels of anticoagulation * Patients with DVT/PE within the past 6 months are eligible provided they receive full anticoagulation during study treatment * No active infection requiring oral or intravenous antibiotics * No uncontrolled illness including, but not limited to, any of the following: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Psychiatric illness or social situations that would preclude study compliance * No known hepatitis B or C * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to lenalidomide or CCI-779 * See Disease Characteristics * Prior lenalidomide allowed * Prior high-dose chemotherapy with stem cell transplantation allowed * More than 4 weeks since prior chemotherapy or other antimyeloma systemic therapy (e.g., thalidomide, bortezomib, or high-dose corticosteroids) and recovered * No prior exposure to both lenalidomide and mTOR inhibitors (given together) * Treatment with single-agent lenalidomide or single-agent mTOR inhibitor allowed * No other concurrent investigational agents * No concurrent corticosteroids unless for physiologic maintenance * No concurrent antiretroviral therapy for HIV-positive patients * No concurrent myeloid growth factors (e.g., filgrastim \[G-CSF\] or sargramostim \[GM-CSF\]) * No concurrent grapefruit or grapefruit juice