Temsirolimus in Treating Patients With Relapsed or Refractory Multiple Myeloma

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