Pilot Study of Sonidegib and Buparlisib in Treating Patients With Advanced or Metastatic Basal Cell Carcinoma

INCLUSION CRITERIA: * Able to understand and sign informed consent * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 * Metastatic BCC, histologic confirmation of distant BCC metastasis * Metastatic disease, target lesion must be measurable using computed tomography (CT) or magnetic resonance imaging (MRI) * Locally advanced BCC are required to have disease that is considered inoperable due to significant functional compromise or to have a medical contraindication to surgery * Nevoid BCC syndrome (Gorlin syndrome) may enroll in this study but must meet the criteria for locally advanced or metastatic disease listed above * COHORT 2 ONLY: A Smoothened inhibitor must have been previously administered as monotherapy * Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L * Platelets ≥ 80 x10\^9/L * Hemoglobin (Hb) \> 9 g/dL or values ≥ lower limit of normal (LLN) for site-specific lab * Total calcium (corrected for serum albumin) within normal limits (biphosphonate use for malignant hypercalcemia control is not allowed) * Magnesium ≥ the lower limit of normal * Potassium within normal limits for the institution * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) within normal range \[or ≤ 3.0 x upper limit of normal (ULN) if liver metastases are present\] * Serum bilirubin within normal range (or ≤ 1.5 x ULN if liver metastases are present; or total bilirubin ≤ 3.0 x ULN with direct bilirubin within normal range in patients with well-documented Gilber…