• Maximum tolerated dose (MTD) of sonidegib in combination with pembrolizumab (Part A) [ Time Frame: Up to 21 days ]
  MTD is defined as the dose level below the lowest dose that induces dose- limiting toxicity (DLT) in at least one-third of patients. Three patients will be treated at a given dose level combination and observed for at least 21 days from start of treatment to assess toxicity.
• Response rate of sonidegib in combination with pembrolizumab (Part B) [ Time Frame: Up to 30 days post treatment ]
  Assessed by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria.

• Incidence of adverse events [ Time Frame: Up to 30 days post treatment ]
  Assessed by National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version (v)5.0. Number of severity of all adverse events will be tabulated and summarized. The grade 3+ adverse events will also be described and summarized in a similar fashion. Overall toxicity incidence as well as toxicity profiles by dose level and patient will be explored and summarized. Frequency distributions, graphical techniques and other descriptive measures will form the basis of these analyses.
• Response profile [ Time Frame: Up to 30 days post treatment ]
  Responses will be calculated based on RECIST 1.1 for this study. Best response is defined to be the best objective status recorded from the start of the treatment until disease progression/recurrence (taking as reference for progressive disease the smallest measurements recorded since the treatment started). Responses will be summarized by simple descriptive summary statistics delineating complete and partial responses as well as stable and progressive disease in this patient population.
• Duration of response (DOR) [ Time Frame: From the date on which an objective response is first determined until the first date on which radiographic disease progression is determined, assessed up to 30 days ]
  Determined only for patients with confirmed response. Participants who achieve a confirmed objective response who have not experienced radiographic or clinical progression will be censored at the date of the last available post-baseline evaluable tumor assessment.
• Disease control rate (DCR) [ Time Frame: At 6 months ]
  Assessed by RECIST v1.1. DCR defined as proportion of participants who achieve complete response (CR), partial response (PR), or stable disease and do not experience subsequent radiographic progressive disease for >= 6 months from the time of treatment initiation.
• Overall survival (OS) [ Time Frame: From study entry to death from any cause, assessed up to 30 days post treatment ]
  Will be estimated using Kaplan-Meier method.
• Progression-free survival (PFS) [ Time Frame: From study entry to the first of either disease progression or death from any cause, assessed up to 30 days post treatment ]
  Disease progression will be determined based on RECIST 1.1 criteria. PFS will be estimated using the Kaplan-Meier method.

• Changes in immune cell markers, cytokines, and soluble PD-L1 [ Time Frame: Baseline up to 30 days post treatment ]
  Will estimate the immunologic effects of sonidegib and pembrolizumab by investigating the changes in immune cell markers, cytokines, and soluble PD-L1 in blood. These changes will be assessed over time and correlated with clinical data as well in an exploratory and hypothesis generating fashion.
• Levels of Bcl-2 interacting mediator of cell death (BIM) [ Time Frame: At baseline ]
  Assessed by flow cytometry.
• Level of serum soluble PDL-1 [ Time Frame: At baseline ]

• Changes in immune cell markers, cytokines, and soluble PD-L1 [ Time Frame: Baseline up to 30 days post treatment ]
  Will estimate the immunologic effects of sonidegib and pembrolizumab by investigating the changes in immune cell markers, cytokines, and soluble PD-L1in blood. These changes will be assessed over time and correlated with clinical data as well in an exploratory and hypothesis generating fashion.
• Levels of Bcl-2 interacting mediator of cell death (BIM) [ Time Frame: At baseline ]
  Assessed by flow cytometry.
• Level of serum soluble PDL-1 [ Time Frame: At baseline ]

PRIMARY OBJECTIVES:

I. To determine the maximum tolerated dose (MTD) of sonidegib in combination with pembrolizumab in participants with advanced solid tumors as part of the dose escalation phase. (Part A) II. To estimate the response rate of sonidegib in combination with pembrolizumab in participants with non-small cell lung cancer (NSCLC) or head and neck squamous cell carcinoma (HNSCC) as part of the expansion cohort based on Response Evaluation Criteria in Solid Tumors (RECIST) criteria. (Part B)

SECONDARY OBJECTIVES:

I. To characterize the safety profile and tolerability of sonidegib and pembrolizumab.

II. To obtain preliminary estimates of efficacy as measured by response rate (based on RECIST criteria), disease control rate at 6 months, duration of response, overall survival (OS), and progression free survival (PFS) of sonidegib and pembrolizumab in patients with selected advanced solid tumors.

CORRELATIVE RESEARCH OBJECTIVES:

I. To estimate the immunologic effects of sonidegib and pembrolizumab by investigating the changes in circulating tumor cells, immune cell markers, cytokines, and soluble PD-L1 in blood.

OUTLINE: This is a dose-escalation study of sonidegib.

Patients receive sonidegib orally (PO) once daily (QD) on days 1-8 and pembrolizumab intravenously (IV) over 30 minutes on day 8. Treatment repeats every 21 days for up to 24 cycles in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up within 30 days.

• Clinical Stage III Cutaneous Melanoma AJCC v8
• Clinical Stage III Gastric Cancer AJCC v8
• Clinical Stage III Gastroesophageal Junction Adenocarcinoma AJCC v8
• Clinical Stage IV Cutaneous Melanoma AJCC v8
• Clinical Stage IV Gastric Cancer AJCC v8
• Clinical Stage IV Gastroesophageal Junction Adenocarcinoma AJCC v8
• Clinical Stage IVA Gastric Cancer AJCC v8
• Clinical Stage IVA Gastroesophageal Junction Adenocarcinoma AJCC v8
• Clinical Stage IVB Gastric Cancer AJCC v8
• Clinical Stage IVB Gastroesophageal Junction Adenocarcinoma AJCC v8
• Locally Advanced Urothelial Carcinoma
• Metastatic Gastric Adenocarcinoma
• Metastatic Gastroesophageal Junction Adenocarcinoma
• Metastatic Head and Neck Squamous Cell Carcinoma
• Metastatic Lung Non-Small Cell Carcinoma
• Metastatic Malignant Solid Neoplasm
• Metastatic Melanoma
• Metastatic Urothelial Carcinoma
• Pathologic Stage III Cutaneous Melanoma AJCC v8
• Pathologic Stage III Gastric Cancer AJCC v8
• Pathologic Stage III Gastroesophageal Junction Adenocarcinoma AJCC v8
• Pathologic Stage IIIA Gastric Cancer AJCC v8
• Pathologic Stage IIIA Gastroesophageal Junction Adenocarcinoma AJCC v8
• Pathologic Stage IIIB Gastric Cancer AJCC v8
• Pathologic Stage IIIB Gastroesophageal Junction Adenocarcinoma AJCC v8
• Pathologic Stage IIIC Gastric Cancer AJCC v8
• Pathologic Stage IV Cutaneous Melanoma AJCC v8
• Pathologic Stage IV Gastric Cancer AJCC v8
• Pathologic Stage IV Gastroesophageal Junction Adenocarcinoma AJCC v8
• Pathologic Stage IVA Gastroesophageal Junction Adenocarcinoma AJCC v8
• Pathologic Stage IVB Gastroesophageal Junction Adenocarcinoma AJCC v8
• Recurrent Head and Neck Squamous Cell Carcinoma
• Refractory Lung Non-Small Cell Carcinoma
• Stage IV Cutaneous Squamous Cell Carcinoma of the Head and Neck AJCC v8
• Stage IV Lung Cancer AJCC v8
• Stage IVA Lung Cancer AJCC v8
• Stage IVB Lung Cancer AJCC v8
• Unresectable Malignant Solid Neoplasm
• Unresectable Melanoma

• Biological: Pembrolizumab
  Given IV
  Other Names:

  • Keytruda
  • Lambrolizumab
  • MK-3475
  • SCH 900475
• Drug: Sonidegib
  Given PO
  Other Names:

  • Erismodegib
  • LDE-225
  • LDE225
  • Odomzo
  • Smoothened Antagonist LDE225

Inclusion Criteria:

• Resolution of adverse events (AEs) from prior treatment to baseline, or Common Terminology Criteria for Adverse Events (CTCAE) =< grade 1 unless AEs are clinically nonsignificant and/or stable with supportive therapy.
• 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 enrolling institution for follow-up (during the active monitoring phase of the study).
• Willing to provide blood samples for correlative research purposes.
• Must be able to swallow capsules and have no significant impairment in gastrointestinal absorption.
• Willing and able to provide informed consent.

• PART A (DOSE ESCALATION): Patient must satisfy all subsets in one of the following:

  • Patients with NSCLC.

    • Pathologically confirmed metastatic non-small cell lung cancer (NSCLC).
    • Patients with EGFR, ALK, or BRAF genomic abnormalities must have also received and progressed on prior Food and Drug Administration (FDA)-approved targeted therapies

  • Melanoma.

    • Unresectable or metastatic melanoma.

      • NOTE: Previous treatment using PD-1/PD-L1 checkpoint inhibitors is allowed.

  • Head and neck squamous cell cancer (HNSCC):

    • Recurrent or metastatic HNSCC with disease progression on or after prior platinum-containing chemotherapy.

      • NOTE: Previous treatment using PD-1/PD-L1 checkpoint inhibitors is allowed.

  • Urothelial carcinoma (locally advanced or metastatic).

    • Newly diagnosed cisplatin ineligible patients. OR
    • Progression during or within 12 months of treatment with platinum-containing agent.

  • Microsatellite instability-high (MSI-H) cancer.

    • Unresectable or metastatic solid tumors that progressed on prior treatment and are MSI-H or mismatch repair deficient.
    • No satisfactory alternative treatment options available. For colorectal cancer, must have progressed following treatment with fluoropyramidine, oxaliplatin, and irinotecan.

  • Gastric or gastroesophageal junction adenocarcinoma

    • Locally advanced or metastatic tumors that express PD-L1 as evidenced by a combined positive score (>= 1) using the PD-L1 immunohistochemistry (IHC) 223C pharmDx test (Dako).
    • Disease progression on 2 or more prior systemic therapies.

• PART B (DOSE EXPANSION) COHORT A: Recurrent or metastatic HNSCC

  • Pathologically confirmed recurrent or metastatic HNSCC

  • Disease progression on or after platinum-containing chemotherapy

    • NOTE: Previous treatment using PD-1/PD-L1 checkpoint inhibitors is allowed.

• PART B ( DOSE EXPANSION) COHORT B: Refractory NSCLC.

  • Pathologically confirmed metastatic non-small cell lung cancer (NSCLC).

  • Disease progression on >= 1 prior line of systemic therapy.

    • NOTE: Previous treatment using PD-1/PD-L1 checkpoint inhibitors is allowed.
  • Patients with EGFR, ALK, or BRAF genomic abnormalities must have also received and progressed on prior FDA-approved targeted therapies.

Exclusion Criteria:

• Any of the following because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects:

  • Pregnant persons.
  • Nursing persons.
  • Persons of childbearing potential and with partners of childbearing potential who are unwilling to employ adequate contraception.
• CTCAE >= grade 3 treatment-emergent adverse event (TEAE) to prior checkpoint inhibitor, TEAE requiring systemic corticosteroids, or permanent treatment discontinuation due to toxicity.
• Neuromuscular disorders (e.g. inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis and spinal muscular atrophy), or a history of rhabdomyolysis.

• Concomitant treatment with drugs that are recognized to cause rhabdomyolysis, including statins.

  • NOTE: Patients taking such medications need to be discontinued at least 2 weeks prior to starting sonidegib treatment. If an agent to control lipids is required, pravastatin may be given with caution.
• Receiving strong inhibitors or inducers of CYP3A4/5, moderate inducers of CYP3A4, and/or grapefruit/grapefruit juice or starfruit products that cannot be discontinued before starting treatment with sonidegib.

NOTE: Medications that are strong CYP3A4/5 inhibitors or inducers, moderate inducers of CYP3A4, and grapefruit/grapefruit juice/starfruit products should be discontinued at least 4 weeks prior to starting treatment with sonidegib.

• Active autoimmune diseases that have required systemic treatment modifications within the past 3 months or that require chronic systemic steroids or immunosuppressive agents.
• Requirement for systemic corticosteroids (> 10 mg daily prednisone equivalent) or other immunosuppressive medications =< 14 days prior to registration.

NOTE: Inhaled or topical steroids, and adrenal replacement steroid doses >10 mg daily prednisone equivalent, are permitted in the absence of active autoimmune disease.

• Life expectancy < 3 months.
• Central nervous system metastases that are untreated, symptomatic, or require steroids.

NOTE: Patients with history of stable treated brain metastases are eligible. Stable treated metastases are defined as follows:

• No evidence of progression for >= 8 weeks on brain imaging (either magnetic resonance imaging [MRI] or computed tomography [CT] scan).
• No corticosteroid use for brain metastases for >= 2 weeks before randomization.

• >= 8 weeks from completion of definitive treatment for brain metastases.

  • Any of the following prior therapies:
• Major surgery =< 4 weeks prior to registration.
• Received any experimental drugs or anti-neoplastic therapy =< 4 weeks prior to receiving the first dose of study treatment
• Received a live vaccine =< 30 days prior to registration

• Unresolved toxicity from prior treatment (subjects must be recovered to baseline or =< grade 1 toxicity from previous anticancer treatments or investigational products)

  • Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens.