Cediranib Maleate and Selumetinib Sulfate in Treating Patients With Solid Malignancies

Inclusion Criteria: * Histologic proof of cancer that is now considered clinically unresectable and for whom there is no standard therapy; NOTE: for the maximum tolerated dose (MTD) expansion cohort only: metastatic melanoma histology is required * Measurable and non-measurable disease are eligible * Ability to provide informed consent * Absolute neutrophil count (ANC) \>= 1500/uL (obtained =\< 21 days prior to registration) * Platelets (PLT) \>= 100,000/uL (obtained =\< 21 days prior to registration) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (obtained =\< 21 days prior to registration) * Aspartate aminotransferase (AST) =\< 2.5 x ULN or =\< 5 x ULN in presence of liver metastases (obtained =\< 21 days prior to registration) * Creatinine =\< 1.5 x ULN (obtained =\< 21 days prior to registration) * Hemoglobin (HgB) \>= 9.0 gm/dL (obtained =\< 21 days prior to registration) * Alkaline phosphatase =\< 2.5 x ULN (obtained =\< 21 days prior to registration) * Creatinine clearance \> 50 ml/min, by either Cockcroft-Gault formula or 24-hour urine collection analysis (obtained =\< 21 days prior to registration) * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 * Willing to return to Mayo for follow up * Life expectancy \>= 12 weeks * Women of childbearing potential only: negative serum pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Expansion phase only: willing to provide blood samples and archived…