CCI-779 in Treating Patients With Soft Tissue Sarcoma or Gastrointestinal Stromal Tumor

Inclusion Criteria: * Histologically or cytologic confirmed soft tissue sarcoma * Measurable disease; for patients having only lesions measuring at least 1 cm to less than 2 cm, must use spiral CT imaging for both pre- and post-treatment tumor assessments * Absolute neutrophil count (ANC) \>= 1,500/μL * Platelets (PLTS) \>= 100,000/μL * Hgb \>= 10.0 g/dL * Direct bilirubin =\< 1.5 x ULN (upper limit normal) * AST(SGOT) =\< 2.5 x ULN or =\< 5 x ULN\* if liver metastases are present * ALT(SGPT) =\< 2.5 x ULN or =\< 5 x ULN\* if liver metastases are present * Creatinine =\< 1.5 x ULN, or if greater, creatinine clearance \>= 50 mL/min/1.73 m\^2 * Baseline glucose levels * Fasting serum cholesterol =\< 350 mg/dL (9.0 mmol/L) * Fasting triglycerides =\< 400 mg/dL (4.56 mmol/L) * ECOG Performance Status (PS) 0, 1 or 2 * Life expectancy \>= 12 weeks * Capable of understanding the investigational nature, potential risks and benefits of the study, and able to provide valid informed consent Exclusion Criteria: * Any of the following as this regimen may be harmful to a developing fetus or nursing child: * Pregnant women * Breast-feeding women * Men or women of childbearing potential or their sexual partners who are unwilling to employ adequate contraception ( diaphragm, birth control pills, injections, intrauterine device \[IUD\], surgical sterilization, subcutaneous implants, or abstinence, etc.) * Any of the following: * Nitrosoureas or mitomycin =\< 6 weeks prior to study entry * Other chemotherapy =\< 4 weeks prior to study entry * Radiotherapy =\< 4 weeks prior to study entry * Concurrent use of any other investigation agent * Adverse events due to agents administered =\< 4 weeks prior to study entry * History of allergic reactions attributed to compounds of similar chemical or biologic composition to CCI-779 * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, diabetes, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Known HIV-positive patients receiving combination anti-retroviral therapy * Prior chemotherapy for metastatic disease * Exceptions: * Patients with GIST who fail Gleevec are eligible * Patients who have had adjuvant/neoadjuvant chemotherapy are also eligible * Known brain metastases * Exception: Patients with treated brain metastatic disease with stable symptoms after treatment for \>= 1 month