Nivolumab With Vismodegib in Patients With Basal Cell Nevus Syndrome

Inclusion Criteria: * 10 or more surgically eligible BCCs (SEBS) within the prior 2 years * Age \> 16 years * Karnofsky Performance Score (KPS) \> 60%, Eastern Cooperative Oncology Group (ECOG) \< 2 * Prior SMO inhibitor therapy is permitted, but patients must have developed new and/or progressive lesions on or after therapy * Adequate organ function * All clinically significant toxicities from prior systemic therapy must be \< Grade 1 * Subjects must agree to undergo four serial tumor biopsies (may be of different tumors) at baseline, after a two week run-in of Vismodegib, between 4-6 weeks of concurrent Nivolumab and Vismodegib, and at the time of disease recurrence or progression. Exclusion Criteria: 1. Prior therapy with an immunological checkpoint inhibitor 2. Prior SMO inhibitor therapy is permitted, but patients must have developed new and/or progressive lesions on or after therapy 3. Routine use of topical (applied to \>5% of skin) or systemic therapies that might interfere with evaluation of the study medication in the prior 4 weeks 1. Topical corticosteroids 2. Systemic or topical retinoids e.g., etretinate, isotretinoin, tazarotene, tretinoin, adapalene 3. Topical alpha-hydroxy acids e.g., glycolic acid, lactic acid 4. Systemic or topical 5-fluorouracil or imiquimod to skin above the knees 4. Patients who have not recovered from adverse events (\> Grade 1) due to prior treatments 5. Treatment with any other investigational agents 6. Recent major surgery within 4 weeks prior to starting study treatment. Minor surgeries such as placement of vascular access are not exclusionary. 7. Known history of hypersensitivity to any of the ingredients in the study medication formulations 8. Requirement for immunosuppressive corticosteroids at doses exceeding 10 mg prednisone daily or equivalent prior to first dose of Nivolumab 9. Ongoing or recent (within 5 years) evidence of significant autoimmune disease at baseline or associated with prior therapy requiring treatment with systemic immunosuppressive treatments with the exception of: 1. Viligo 2. Childhood asthma that has resolved 3. Residual endocrinopathies requiring replacement therapy 4. Psoriasis that does not require systemic treatment 10. History of solid organ transplant 11. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements 12. Uncontrolled hypocalcemia, hypomagnesemia, or hypokalemia 13. HIV positive patients on combination antiretroviral therapy 14. Refractory nausea and vomiting, active gastrointestinal disease e.g. inflammatory bowel disease, or significant bowel resection that would preclude adequate absorption 15. Have evidence of any other significant skin condition, clinical disorder, physical examination finding, or laboratory finding that, as judged by the investigator, makes it undesirable for the patient to participate in the study 16. Active treatment for a second malignancy 17. Pregnant women are excluded from this study because nivolumab, ipilimumab and vismodegib may be teratogenic or have abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with nivolumab, ipilimumab or vismodegib, breastfeeding should be discontinued if the mother is receiving study treatment. 18. Male patients unwilling or unable to comply with pregnancy prevention measures