Everolimus and Vatalanib in Treating Patients With Advanced Solid Tumors

Inclusion Criteria: * Histologic proof of cancer that is now unresectable (solid tumors, excluding lymphoma) * Ability to provide informed consent * Willingness to return to Mayo Clinic Rochester for follow up * Life expectancy \>= 12 weeks * Prior anti-VEGF therapy allowed * Cohort IIA: Patients meeting other eligibility criteria, regardless of histopathologic diagnosis; tumor that is amenable to biopsy; willingness to provide blood specimens, undergo DCE-MRI, and undergo brachial artery ultrasound measurements as required by the protocol * The following laboratory values obtained =\< 14 days prior to registration: Negative for proteinuria based on dip stick reading OR, if documentation of +1 result for protein on dip stick reading, then total urinary protein =\< 500 mg and measured creatinine clearance (CrCl) \>= 50 mL/min from a 24-hour urine collection * Cohort IIB: Patients meeting other eligibility criteria AND with pathologic diagnosis of metastatic kidney cancer, neuroendocrine carcinoma, melanoma, and NSCLC; willingness to provide blood specimens required and undergo brachial artery ultrasound measurements * The following laboratory values obtained =\< 14 days prior to registration: ANC \>= 1500/uL; Hgb \>= 9 g/dL; PLT \>= 100,000/uL; Total bilirubin =\< 1.5 x upper limit of normal (ULN); AST =\< 3 x ULN or AST =\< 5 x ULN if liver involvement; Creatinine =\< 1.5 x ULN; INR =\< 1.4 (Cohort IIA only) Exclusion Criteria: * Any of the following prior therapies: Fu…