CCI-779 and Bevacizumab in Treating Patients With Metastatic or Unresectable Kidney Cancer

Inclusion Criteria: * Histologically confirmed metastatic or unresectable renal cell cancer * Must have a component of conventional clear cell histology * The following histologies are excluded: * True papillary * Sarcomatoid features without any clear cell component * Chromophobe * Oncocytoma * Collecting duct tumors * Transitional cell carcinoma * Measurable disease, defined as ≥ 1 lesion ≥ 2.0 cm in the longest diameter by conventional techniques OR ≥ 1.0 cm by spiral CT scan * Tumor tissue (from primary tumor or metastases) available AND patient is willing to donate blood for research studies (phase II only) * No CNS metastases by head CT scan or MRI * Performance status - ECOG 0-2 * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Hemoglobin ≥ 9.0 g/dL * No evidence of bleeding diathesis or coagulopathy * No history of clinically significant bleeding or active bleeding * Bilirubin ≤ 1.5 times upper limit of normal (ULN) * Alkaline phosphatase ≤ 2.5 times ULN (5 times ULN if liver metastases are present) * AST ≤ 2.5 times ULN (5 times ULN if liver metastases are present) * PT/INR ≤ 1.5 * Patients on full-dose warfarin or stable-dose low molecular weight heparin must have INR \> 1.5 but ≤ 3 * Creatinine ≤ 1.5 times ULN * Urine protein ≤ 1+ by dipstick or urinalysis * Urine protein \< 1,000 mg on a 24-hour urine collection * No cerebrovascular accident within the past 6 months * No peripheral vascular disease with claudication on \< 1 block * No New York Heart Association class II-IV congestive heart failure * No angina pectoris requiring nitrate therapy * No myocardial infarction within the past 6 months * No uncontrolled hypertension, defined as systolic blood pressure (BP) ≥ 160 mm Hg and/or diastolic BP ≥ 90 mm Hg despite medication * No cardiac arrhythmias * No other significant cardiovascular disease * No ongoing hemoptysis * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for at least 3-4 months after study participation * Fasting cholesterol ≤ 350 mg/dL * Triglycerides ≤ 1.5 times ULN (may achieve using lipid lowering agents) * No known hypersensitivity to recombinant human antibodies * No significant traumatic injury within the past 4 weeks * No serious or non-healing wound, ulcer, or bone fracture * No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 4 weeks * No pathological conditions that confer a high risk of bleeding (e.g., tumor involving major vessels or known varices) * No diabetes * No other currently active malignancy except nonmelanoma skin cancer * Patients are not considered to have a currently active malignancy if they have completed anticancer therapy AND are considered to be at \< 30% risk of relapse * No other uncontrolled serious medical or psychiatric condition * At least 4 weeks since prior biologic response modifiers for metastatic disease * No prior bevacizumab or mTOR inhibitors * At least 4 weeks since prior chemotherapy for metastatic disease * Prior palliative radiotherapy to metastatic lesions allowed provided there is ≥ 1 measurable and/or evaluable lesion that has not been irradiated * At least 4 weeks since prior and no concurrent radiotherapy * Prior nephrectomy allowed * More than 4 weeks since prior major surgery or open biopsy * More than 1 week since prior core biopsy * No concurrent major surgery * At least 4 weeks (2 weeks for vascular endothelial growth factor \[VEGF\] receptor tyrosine kinase inhibitor \[RTKI\] therapy) since prior and no more than 2 therapies (phase II) * One of these therapies must have included a RTKI agent administered for a minimum of 4 weeks * Concurrent full-dose warfarin or low molecular weight heparin allowed provided dose is stable AND INR requirements are met * Concurrent zoledronate for bone metastases and/or hypercalcemia allowed provided therapy was initiated prior to study entry