This randomized phase III trial studies giving everolimus together with bevacizumab to see how well it works compared to everolimus alone in treating patients with advanced kidney cancer that progressed after first-line therapy. Everolimus may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Monoclonal antibodies, such as bevacizumab, can interfere with tumor growth by blocking the ability of tumor cells to grow and spread. Everolimus and bevacizumab may also stop the growth of kidney cancer by blocking blood flow to the tumor. It is not yet known whether giving everolimus together with bevacizumab is better than everolimus alone in treating patients with advanced kidney cancer that has progressed after first-line therapy.

PRIMARY OBJECTIVES: l. To compare the overall survival of patients receiving bevacizumab plus everolimus and everolimus alone among patients with advanced renal cell carcinoma progressing after first line vascular epidermal growth factor receptor (VEGFR)-tyrosine kinase inhibitor (TKI) treatment. SECONDARY OBJECTIVES: I. To compare the progression-free survival and proportion who experience an objective response (defined as complete clinical response \[cCR\] + partial response \[PR\]) in patients with advanced renal cell carcinoma receiving bevacizumab plus everolimus and everolimus alone. II. To compare grade 3 or higher toxicity in patients receiving each treatment regimen. OUTLINE: Patients are randomized to 1 of 2 treatment arms. ARM I: Patients receive everolimus orally (PO) once daily (QD) on days 1-28. ARM II: Patients receive everolimus PO QD on days 1-28 and bevacizumab intravenously (IV) over 30-90 minutes on days 1 and 15. In both arms, courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 8 weeks until disease progression and then every 6 months for up to 5.5 years.