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This phase II trial is studying how well temsirolimus works in treating patients with relapsed or refractory multiple myeloma. Drugs used in chemotherapy such as temsirolimus work in different ways to stop cancer cells from dividing so they stop growing or die. PRIMARY OBJECTIVES: I. Determine the overall response rate in patients with relapsed or refractory multiple myeloma treated with CCI-779. SECONDARY OBJECTIVES: I. Determine the progression-free survival of patients treated with this drug. II. Determine the toxicity of this drug in these patients. III. Determine the presence of PTEN mutation in patients treated with this drug. IV. Correlate the pharmacokinetics of this drug with response in these patients. V. Correlate the pharmacodynamic effects of this drug with response in these patients. OUTLINE: This is an open-label study. Patients receive temsirolimus IV over 30 minutes on days 1, 8, 15, and 21. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.
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
is designated in this study