Everolimus in Combination With Imatinib Mesylate in Treating Patients With Locally Advanced, Locally Recurrent, or Metastatic Soft Tissue Sarcoma

Inclusion Criteria: * Histologically or cytologically confirmed synovial sarcoma that is platelet-derived growth factor receptor, alpha polypeptide positive (PDGFRA+) * Metastatic and/or locally advanced or locally recurrent disease * Patients must consent to tumor biopsies before therapy and after the second week of therapy * Patients who do not have accessible tumor for biopsy may be enrolled at the discretion of the principal investigator * Patients must have measurable disease, by RECIST 1.1, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 20 mm by conventional techniques or as ≥ 10 mm by spiral CT scan * Tumor lesions that are situated in a previously irradiated area may be considered measurable for the purposes of this study only if there is evidence of growth of the area following a course of irradiation that cannot be attributed to necrosis or bleeding into the tumor * Patients with brain metastasis that has been treated with definitive surgery or radiotherapy, and who have been clinically stable for 3 months following the procedure with no neurological signs or symptoms and no requirement for systemic glucocorticoids, are eligible for study * ECOG performance status 0-1 * Life expectancy greater than 3 months * ANC ≥ 1,500/mm³ * Platelet count ≥ 75,000/mm³ * Total bilirubin ≤ 1.5 times upper limit of normal (ULN) (except for patients with known Gilbert syndrome) * AST/ALT ≤ 3 times ULN * Serum creatinine ≤ 1.5 times ULN * Serum glucose ≤ 120 mg/dL * Total cholesterol \< 300 mg/dL * Triglycerides \< 2.5 times ULN * Not pregnant or nursing * Negative pregnancy test * Women of child-bearing potential and men must agree to use adequate contraception (hormonal, barrier method of birth control, or abstinence) during therapy and for at least 8 weeks after completion of therapy * Patients must not have current evidence of another malignancy * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to everolimus, imatinib mesylate, or other agents used in the study * No uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, including HIV, active hepatitis B or C, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, poorly controlled diabetes, or psychiatric illness/social situations that would limit compliance with study requirements * No patients with significant compromised respiratory problems or an active and unexplained pneumonitis * No concurrent combination antiretroviral therapy for HIV-positive patients * At least 4 weeks since any number of prior chemotherapy regimens (6 weeks for carmustine or mitomycin C) for recurrent/metastatic disease * No prior tyrosine kinase inhibitors * Recovered to ≤ grade 1 NCI CTCAE version 4 adverse events related to prior tumor-specific therapy * No patients who have had major surgery within the past 4 weeks, or who have not recovered from adverse events to ≤ grade 1 NCI CTCAE adverse events associated with surgery * Surgical changes not expected to improve ( e.g., removal of muscle tissue) allowed * No prior mTOR inhibitors, such as sirolimus, everolimus, ridaforolimus, or temsirolimus * No other concurrent investigational agents