Everolimus and Bevacizumab in Advanced Non-Clear Cell Renal Cell Carcinoma (RCC)

Inclusion Criteria: * Advanced renal cell carcinoma of non-clear cell histology, histologically with papillary features confirmed by MSKCC pathology. Availability of additional tissue for correlative studies is NOT in inclusion requirement. * Evidence of unidimensionally measurable disease per RECIST 1.1 (Eisenhauer, Therasse et al. 2009). Resolution of all acute toxic effects of prior radiotherapy or surgical procedures to NCI CTCAE Version 4.0 grade ≤1. * Adequate organ function as defined by the following criteria: * Absolute neutrophil count (ANC) ≥1,500/μL * Platelets ≥100,000/μL * Hemoglobin ≥9.0 g/dL * Serum calcium ≤12.0 mg/dL * Serum creatinine ≤1.5 x ULN * Total serum bilirubin ≤2.0 x ULN * Serum aspartate transaminase (AST; serum glutamic oxaloacetic transaminase \[SGOT\]) and serum alanine transaminase (ALT; serum glutamic pyruvic transaminase \[SGPT\]) ≤2.5 x local laboratory upper limit of normal (ULN), or AST and ALT ≤5 x ULN if liver function abnormalities are due to underlying malignancy * INR ≤1.5. (Anticoagulation is allowed if target INR ≤ 1.5 on a stable dose for \>2 weeks at time of study entry.) * Fasting serum cholesterol ≤300 mg/dL OR ≤7.75 mmol/L AND fasting triglycerides ≤ 2.5 x ULN. NOTE: In case one or both of these thresholds are exceeded, the patient can only be included after initiation of appropriate lipid lowering medication. Karnofsky performance status ≥ 70 %. * 18 years of age or older. * Ability to swallow oral medication. * Signed and dated informed consent document indicating that the subject (or legally acceptable representative) has been informed of all pertinent aspects of the trial prior to undergoing study screening procedures. * Subject's willingness and ability to comply with scheduled visits, treatment plans, laboratory tests, and other study procedures. Exclusion Criteria: * Patients who have received prior systemic therapy for their RCC with VEGF pathway inhibitor (such as sunitinib, sorafenib, and bevacizumab) or with mTOR inhibitors (such as sirolimus, temsirolimus, everolimus, or deforolimus). * Patients within 28 days post major surgery (e.g., intra-thoracic, intra-abdominal or intra-pelvic), open biopsy, or significant traumatic injury to avoid wound healing complications. Minor procedures and percutaneous biopsies or placement of vascular access device without complications require 48 hours prior to study entry. * Patients who had radiation therapy within 28 days prior to start of study treatment (palliative radiotherapy to bone lesions allowed if completed 2 weeks prior to study treatment start). Patients with evidence or history of central nervous system (CNS) metastases or spinal cord compression, unless prior treatment with surgery or radiotherapy AND no progression of CNS disease within 6 months prior to enrollment. * Patients with a history of abdominal fistula, gastrointestinal perforation, or intraabdominal abscess within 6 months prior to study enrollment. * Patients with proteinuria on screening urinalysis confirmed to be \>1g /24h by 24 hour urine collection. * Patients with inadequately controlled hypertension (defined as a blood pressure of \> 150 mmHg systolic and/or \> 100 mmHg diastolic on medication), or any prior history of hypertensive crisis or hypertensive encephalopathy. Patients receiving chronic systemic treatment with corticosteroids (dose of ≥ 10 mg/day methylprednisone equivalent) or another immunosuppressive agent. Inhaled and topical steroids are acceptable. * Patients with a known history of HIV seropositivity. * Patients who have any severe and/or uncontrolled medical conditions or other conditions that could affect their participation in the study such as: * unstable angina pectoris (at any time), symptomatic congestive heart failure (NYHA III, IV) (at any time), serious uncontrolled cardiac arrhythmia (at any time), myocardial infarction, cerebrovascular accidents, or symptomatic left ventricular dysfunction ≤ 6 months prior to first study treatment * active bleeding diathesis * known severely impaired lung function defined as spirometry and DLCO ≤ 50% of normal and oxygen saturation at rest ≤ 88% on room air. * symptomatic intrinsic lung disease requiring oxygen supplementation at baseline * Uncontrolled diabetes mellitus as defined by HbA1c \>8% despite adequate therapy. Patients with a known history of impaired fasting glucose or diabetes mellitus (DM) may be included, however blood glucose and antidiabetic treatment must be monitored closely throughout the trial and adjusted as necessary * any active (acute or chronic) or uncontrolled infection/disorders that impair the ability to evaluate the patient or for the patient to complete the study * liver disease such as cirrhosis decompensated liver disease or active and chronic hepatitis (i.e. quantifiable HBV-DNA and/or positive HBsAg, quantifiable HCV-RNA). * Patients who have a history of another primary malignancy and are off treatment for ≤ 3 years, with the exception of non-melanoma skin cancer and carcinoma in situ of the uterine cervix. * Female patients who are pregnant or breast feeding * Women of child-bearing potential (WOCBP), defined as all women physiologically capable of becoming pregnant, must use highly effective methods of contraception during the study and 8 weeks after. Highly effective contraception methods include combination of any two of the following: 1. Use of oral, injected or implanted hormonal methods of contraception or; 2. Placement of an intrauterine device (IUD) or intrauterine system (IUS); 3. Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/ vaginal suppository; 4. Total abstinence or; 5. Male/female sterilization * Women are considered post-menopausal and not of child-bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks prior to randomization. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child-bearing potential. * Male patients whose sexual partner(s) are WOCBP who are not willing to use adequate contraception, during the study and for 8 weeks after the end of treatment * Patients who are using other investigational agents or who had received investigational drugs ≤ 4 weeks prior to study treatment start. * Patients who have received attenuated live vaccines within one week of study entry. Examples of live vaccines include intranasal influenza, measles, mumps, rubella, oral polio, BCG, yellow fever, varicella and TY21a typhoid vaccines. Known intolerance or hypersensitivity to Everolimus or other rapamycin analogs (e.g. sirolimus, temsirolimus). * Known impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of oral Everolimus. * Patients with a history of non-compliance to medical regimens or who are considered potentially unreliable or will not be able to complete the entire study