Temsirolimus and Imatinib Mesylate in Treating Patients With Chronic Myelogenous Leukemia

Inclusion Criteria:

* Histologically confirmed chronic myelogenous leukemia (CML)

  * Philadelphia chromosome-positive OR Bcr-Abl-positive disease, meeting 1 of the following criteria:

    * Accelerated phase, defined by at least 1 of the following:

      * 10-19% blasts in the peripheral blood or bone marrow
      * At least 20% basophils in peripheral blood or bone marrow
      * Platelet count \< 100,000/mm\^3 (unrelated to therapy)
      * Platelet count \> 1,000,000/mm\^3 (unresponsive to therapy)
      * Increasing splenomegaly AND increasing WBC count (unresponsive to therapy)
      * Clonal evolution
    * Blast phase, defined by 1 of the following:

      * At least 20% blasts in peripheral blood or bone marrow
      * Extramedullary disease
    * Chronic phase, defined by all of the following:

      * Less than 10% blasts in peripheral blood or bone marrow
      * Less than 20% basophils in peripheral blood or bone marrow
      * Platelet count \> 100,000/mm\^3
      * Absence of clonal evolution
* May have received and/or failed prior imatinib mesylate therapy

  * Patients not previously treated with imatinib mesylate receive oral imatinib mesylate once daily 14 days before beginning study drug

    * Must be able to tolerate 600 mg per day of imatinib mesylate before starting CCI-779
  * Patients with chronic phase disease must have failed prior imatinib mesylate at a dose ≥ 600 mg/day, as defined by 1 of the following:

    * Must not have achieved or must have lost hematologic response within 3 months after the start of imatinib mesylate
    * Must not have achieved or must have lost cytogenetic response after 6 months of treatment with imatinib mesylate
    * Must not have achieved or must have lost major cytogenetic response after 12 months of treatment with imatinib mesylate
    * Must have lost complete cytogenetic response
* Bone marrow aspirate and biopsy with cytogenetics and fluorescent in situ hybridization confirming t(9;22) completed within the past 28 days
* Performance status - SWOG 0-2
* More than 3 months
* See Disease Characteristics
* Bilirubin normal
* AST and ALT \< 2.5 times upper limit of normal (ULN) (5 times ULN if suspected liver involvement with leukemia)
* Creatinine normal
* Creatinine clearance \> 60 mL/min
* No symptomatic congestive heart failure
* No unstable angina pectoris
* No cardiac arrhythmia
* Ejection fraction ≥ 50% by echocardiogram or MUGA scan for patients with known positive cardiac history (e.g., heart failure, coronary artery disease, cardiomegaly on prior chest x-ray, or valvular heart disease)
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception
* Fasting cholesterol ≤ 350 mg/dL
* Fasting triglycerides ≤ 400 mg/dL
* No history of allergic reaction attributed to compounds of similar chemical or biologic composition to temsirolimus or imatinib mesylate
* No active or ongoing infection
* No psychiatric illness or social situation that would preclude study compliance
* No other active malignancy except nonmelanoma skin cancer
* No other uncontrolled illness
* At least 48 hours since prior interferon alfa for CML
* At least 6 weeks since prior stem cell transplantation
* No concurrent biologic agents
* No concurrent prophylactic colony-stimulating factors
* At least 24 hours since prior hydroxyurea for CML
* At least 7 days since prior mercaptopurine or vinca alkaloids for CML
* At least 7 days since prior low-dose cytarabine (\< 30 mg/m\^2 every 12-24 hours) for CML
* At least 14 days since prior homoharringtonine for CML
* At least 14 days since prior moderate-dose cytarabine (100-200 mg/m\^2 for 5-7 days) for CML
* At least 21 days since prior anthracyclines, mitoxantrone, cyclophosphamide, etoposide, or methotrexate for CML
* At least 28 days since prior high-dose cytarabine (1-3 g/m\^2 every 12-24 hours for 6-12 doses) for CML
* At least 6 weeks since prior busulfan for CML
* No concurrent hydroxyurea
* No other concurrent chemotherapy
* At least 7 days since prior steroids for CML
* No prior organ transplantation
* More than 2 weeks since prior major surgery (e.g., thoracotomy or intra-abdominal surgery)
* Recovered from all prior therapy
* Prior experimental therapy allowed provided completion of treatment corresponds to a duration \> 5 half-lives of the experimental drug or any known active metabolite before study
* No concurrent cyclosporine
* No concurrent anagrelide
* No concurrent oral anticoagulants, including warfarin
* No concurrent CYP3A4 inducers or inhibitors
* No concurrent tacrolimus
* No concurrent plasmapheresis
* No concurrent combination antiretroviral therapy for HIV-positive patients
* No other concurrent investigational agents
* No other concurrent anticancer therapies