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 Gilbert Syndrome) * Serum creatinine ≤ 1.5 x ULN or 24-hour clearance ≥ 50 mL/min * Serum amylase ≤ ULN * Serum lipase ≤ ULN * Fasting plasma glucose ≤ 120 mg/dL (6.7 mmol/L) * Negative serum pregnancy test within 72 hours before starting study treatment in women with childbearing potential * International normalized ratio (INR) ≤ 2 EXCLUSION CRITERIA: * Prior treatment with a P13K inhibitor * Known hypersensitivity to buparlisib or to its excipients * Untreated brain metastases are excluded; however, patients with metastatic central nervous system (CNS) tumors may participate in this trial, if the patient is \> 4 weeks from therapy completion (including radiation and/or surgery), is clinically stable at the time of study entry and is not receiving corticosteroid therapy * Acute or chronic liver, renal disease or pancreatitis * Baseline creatinine kinase (CK) \> ULN * The following mood disorders as judged by the Investigator or a psychiatrist, or as a result of patient's mood assessment questionnaire: * Medically documented history of or active major depressive episode, bipolar disorder (I or II), obsessive-compulsive disorder, schizophrenia, a history of suicidal attempt or ideation, or homicidal ideation (immediate risk of doing harm to others) * ≥ Common Terminology Criteria for Adverse Events (CTCAE) grade 3 anxiety * Meets the cut-off score of ≥ 12 in the Patient Health Questionnaire (PHQ)-9 or a cut-off of ≥ 15 in the Generalized Anxiety Disorder 7-item (GAD-7) mood scale, respectively, or selects a positive response of "1, 2, or 3" to question number 9 regarding potential for suicidal thoughts in the PHQ-9 (independent of the total score of the PHQ-9) * Diarrhea ≥ CTCAE grade 2 * Active cardiac disease including any of the following: * Left ventricular ejection fraction (LVEF) \< 50% as determined by multiple gated acquisition (MUGA) scan or echocardiogram (ECHO) * QTc \> 450 msec on screening electrocardiogram (ECG) (using the QTcF formula) * Angina pectoris that requires the use of anti-anginal medication * Ventricular arrhythmias except for benign premature ventricular contractions * Supraventricular and nodal arrhythmias requiring a pacemaker or not controlled with medication * Conduction abnormality requiring a pacemaker * Valvular disease with document compromise in cardiac function * Symptomatic pericarditis * Patient has a history of cardiac dysfunction including any of the following: * Myocardial infraction within the last 6 months, documented by persistent elevated cardiac enzymes or persistent regional wall abnormalities on assessment of LVEF function * History of documented congestive heart failure (New York Heart Association functional classification 3-4) * Documented cardiomyopathy * Patient has poorly controlled diabetes mellitus \[defined as hemoglobin A1C (HgA1c) \> ULN\], steroid-induced diabetes mellitus, or insulin dependent diabetes mellitus * Other concurrent severe and/or uncontrolled concomitant medical conditions (eg, active or uncontrolled infection) that could cause unacceptable safety risks or compromise compliance with the protocol * Significant symptomatic deterioration of lung function; if clinically indicated, pulmonary function tests including measures of predicted lung volumes, diffusing capacity of the lung for carbon monoxide (DLco), oxygen (O2) saturation at rest on room air should be considered to exclude pneumonitis or pulmonary infiltrates * Impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of buparlisib (eg, ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection); patients with unresolved diarrhea will be excluded as previously indicated * Patients who have been treated with any hematopoietic colony-stimulating growth factors (eg, filgrastim (granulocyte-colony stimulating factor, G-CSF), sargramostim (granulocyte-macrophage colony-stimulating factor, GM-CSF) ≤ 2 weeks prior to starting study drug; erythropoietin or darbepoetin therapy, if initiated at least 2 weeks prior to enrollment, may be continued * Patients who are currently receiving treatment with medication with a known risk to prolong the QT interval or inducing Torsades de Pointes and the treatment cannot either be discontinued or switched to a different medication prior to starting study drug * Patients receiving chronic treatment with steroids or another immunosuppressive agent * Note: topical applications (eg, rash), inhaled sprays (eg, obstructive airways diseases), eye drops or local injections (eg, intr-articular) are allowed; patients with previously treated brain metastases, who are on stable low dose corticosteroids treatment (eg, dexamethasone 2 mg/day, prednisolone 10 mg/day) for at least 14 days before start of study treatment are eligible * Patients who have taken herbal medications and certain fruits within 7 days prior to starting study drug; herbal medications include, but are not limited to St. John's Wort, Kava, ephedra (ma huang), dehydroepiandrosterone (DHEA), gingko biloba, yohimbe, saw palmetto, and ginseng; fruits include the cytochrome P450, family 3, subfamily A (CYP3A) inhibitors Seville oranges, grapefruit, pummelos, or exotic citrus fruits * Patients who are currently treated with drugs known to be moderate and strong inhibitors or inducers of isoenzyme CYP3A, and the treatment cannot be discontinued or switched to a different medication prior to starting study drug; please note that co-treatment with weak inhibitors of CYP3A is allowed * Patients who have received chemotherapy or targeted anticancer therapy ≤ 4 weeks (6 weeks for nitrosourea, antibodies or mitomycin-C) prior to starting study drug must recover to a grade 1 before starting the trial * Patients who have received any continuous or intermittent small molecule therapeutics (excluding monoclonal antibodies) ≤ 5 effective half lives prior to starting study drug or who have not recovered from side effects of such therapy * Use of statin drugs or other medications known to associate with rhabdomyolysis; these drugs must be discontinued at enrollment * Patients who have received wide field radiotherapy ≤ 4 weeks or limited field radiation for palliation ≤ 2 weeks prior to starting study drug or who have not recovered from side effects of such therapy * Patients who have undergone major surgery ≤ 2 weeks prior to starting study drug or who have not recovered from side effects of such therapy * Patients who are currently taking therapeutic doses of warfarin sodium or any other coumadin-derivative anticoagulant; low molecular weight heparin is allowed * Women who are pregnant or breast feeding or adults of reproductive potential not employing an effective method of birth control; double barrier contraceptives must be used through the trial by both sexes; oral, implantable, or injectable contraceptives may be affected by cytochrome P450 interactions, and are therefore not considered effective for this study; women of child-bearing potential, defined as sexually mature women who have not undergone a hysterectomy or who have not been naturally postmenopausal for at least 12 consecutive months (ie, who has had menses any time in the preceding 12 consecutive months), must have a negative serum pregnancy test ≤ 72 hours prior to initiating treatment * Women are considered post-menopausal and not of child bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (eg, age appropriate, history of vasomotor symptoms) or 6 months of spontaneous amenorrhea with serum follicle stimulating hormone (FSH) levels \> 40 mIU/mL (for US only: and estradiol \< 20 pg/mL) or have had surgical bilateral oophorectomy (with or without hysterectomy) at least 6 weeks prior; in the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child bearing potential * Women of child-bearing potential, defined as all women physiologically capable of becoming pregnant, must use highly effective contraception during the study and through 20 months after the final dose of study treatment; for males with partners with childbearing potential, highly effective contraception is required for 6 months; the highly effective contraception is defined as either: * True abstinence: when this is in line with the preferred and usual lifestyle of the subject; periodic abstinence (eg, calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception * Sterilization: have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks ago; in case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment * Male partner sterilization (with the appropriate post-vasectomy documentation of the absence of sperm in the ejaculate); for female subjects on the study, the vasectomized male partner should be the sole partner for that patient * Use of a combination of any two of the following (a+b): * a. Placement of an intrauterine device (IUD) or intrauterine system (IUS) * b. Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository * Oral contraception, injected or implanted hormonal methods are not allowed * Fertile males, must use highly effective (double barrier) methods of contraception (eg, spermicidal gel plus condom) for the entire duration of the study, and continuing using contraception and refrain from fathering a child for 6 months following the study drug; a condom is required to be used also by vasectomized men as well as during intercourse with a male partner in order to prevent delivery of the study treatment via seminal fluid; female partner of male study subject should use highly effective contraception during dosing of any study agent and for 16 weeks after final dose of study therapy * Note: hormonal contraception methods (eg, oral, injected, implanted) are not allowed * Note: woman are considered post-menopausal and not child bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (eg, age appropriate, history of vasomotor symptoms) or six months of spontaneous amenorrhea with serum FSH levels \> 40 mIU/mL and estradiol \< 20 pg/mL or have had surgical bilateral oophorectomy (with or without hysterectomy) at least six weeks ago; in the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child bearing potential * Known diagnosis of human immunodeficiency virus (HIV) infection, hepatitis B or hepatitis C * History of another malignancy within 3 years, except cured basal cell carcinoma of the skin or excised carcinoma in situ of the cervix * Patient is unable or unwilling to abide by the study protocol or cooperate fully with the investigator