Sonidegib and Pembrolizumab in Treating Patients With Advanced Solid Tumors

Inclusion Criteria: * Age \>= 18 years * Measurable disease by RECIST criteria. * Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 or 1. * Hemoglobin \>= 9.0 g/dL (obtained =\< 28 days prior to registration). * Absolute neutrophil count (ANC) \>= 1000/mm\^3 (obtained =\< 28 days prior to registration). * Platelet count \>= 100,000/mm\^3 (obtained =\< 28 days prior to registration). * Total bilirubin =\< 1.5 x upper limit of normal (ULN) OR direct bilirubin =\< ULN (obtained =\< 28 days prior to registration). * Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 2.5 x ULN (=\< 5 x ULN for patients with liver involvement) (obtained =\< 28 days prior to registration). * Creatinine phosphokinase (CK) =\< 2.5 x ULN (obtained =\< 28 days prior to registration). * Serum creatinine =\< 1.5 x ULN or calculated creatinine clearance \>= 50 ml/min using the Cockcroft-Gault formula (obtained =\< 28 days prior to registration). * Negative serum pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only. * Patients of childbearing potential agree to use two forms of medically approved contraception while taking the study drug and for 20 months following the last dose of study drug. Patients with partners of childbearing potential agree to use condoms, even after vasectomy, to avoid potential drug exposure to partner during study drug and for 8 months following the last dose of study drug. * Willing to return to en…