Everolimus and Imatinib Mesylate in Treating Patients With Chronic Phase Chronic Myelogenous Leukemia Who Are Not in Complete Cytogenetic Remission After Previous Imatinib Mesylate

DISEASE CHARACTERISTICS: * Histologically confirmed chronic myelogenous leukemia (CML) * In chronic phase * Philadelphia chromosome (Ph)-positive * No accelerated or blastic phase * Accelerated phase CML is defined as ≥ 15% but \< 30% blasts in peripheral blood or bone marrow OR ≥ 30% blasts and promyelocytes in peripheral blood or bone marrow provided that \< 30% blasts were present OR ≥ 20% peripheral basophils OR platelet count \< 100,000/mm\^3, unrelated to therapy * No less than 20 metaphases in the bone marrow sample * No evidence of complete cytogenetic response to imatinib mesylate (complete cytogenetic response defined as 0% Ph-positive cells in bone marrow) * Receiving continuous imatinib mesylate therapy for ≥ the past 9 months * Dosage ≥ 600 mg/day for ≥ the past 3 months * Stable dose of 600 mg/day for ≥ the past 4 weeks * Achieved and maintained hematological response to imatinib mesylate as defined by all of the following: * WBC \< 20,000/mm\^3 * Basophils \< 20% * Less than 5% myelocytes and metamyelocytes in peripheral blood * No blasts or promyelocytes in peripheral blood * No evidence of disease-related symptoms or extramedullary disease, including enlarged spleen or liver PATIENT CHARACTERISTICS: Age * 18 and over Performance status * WHO 0-2 Life expectancy * Not specified Hematopoietic * See Disease Characteristics * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Hemoglobin ≥ 9 g/dL Hepatic * AST and ALT \< 1.5 times upper limit of normal (ULN) * Bilirubin \< 1.5 times ULN (except for patients with Gilbert's disease) * PTT \< 1.5 times ULN (except for patients on oral anticoagulation therapy) * INR \< 1.5 times ULN (except for patients on oral anticoagulation therapy) Renal * Creatinine \< 1.5 times ULN Cardiovascular * No angina * No New York Heart Association class III or IV cardiac disease Other * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective barrier contraception during and for 3 months after study participation * HIV negative * No history of non-compliance with medical regimens * No hypercholesterolemia or hypertriglyceridemia (fasting state) ≥ grade 2 (despite lipid-lowering therapy) * No diabetes mellitus * No thyroid dysfunction * No neuropsychiatric disorders * No infection * No other severe and/or uncontrolled medical condition that would preclude study participation * No other malignancy within the past 5 years except adequately treated basal cell or squamous cell skin cancer or carcinoma in situ of the cervix PRIOR CONCURRENT THERAPY: Biologic therapy * No prior allogeneic, syngeneic, or autologous bone marrow transplantation or stem cell transplantation for CML * No concurrent prophylactic hematopoietic growth factors (e.g., filgrastim \[G-CSF\], sargramostim \[GM-CSF\], or epoetin alfa) Chemotherapy * No prior chemotherapy regimens used in transplantation Endocrine therapy * Not specified Radiotherapy * Not specified Surgery * Recovered from prior major surgery Other * No prior sirolimus in combination with imatinib mesylate * At least 4 weeks since prior investigational agents used in combination with imatinib mesylate and recovered * No other concurrent investigational therapies * No other concurrent anticancer agents