Pembrolizumab, INCB081776, and Radiation Therapy for Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: * Participants must have histologic or cytologic evidence of head and neck squamous cell carcinoma (HNSCC) that is metastatic or recurrent and therefore considered incurable. Cutaneous skin squamous cell carcinomas located in the head and neck region are eligible after discussion with the Sponsor-Investigator. * Measurable disease that are considered non-amenable to surgery or other curative treatments or procedures, with at least 1 target lesion available for evaluation. * The preference is for measurable disease to be selected from a site that has not received any prior radiation or locoregional therapy. However, if a tumor lesion is situated in a previously irradiated area, or in an area subjected to other prior locoregional therapy, the lesion should demonstrate disease progression after the prior treatment. * Prior cancer treatment must be completed at least 14 days prior to enrollment (for chemotherapy, targeted small molecular therapy, or radiation therapy. Prior treatment with a monoclonal antibody must be completed at least 28 days prior to enrollment. Participants must have recovered from all reversible acute toxic effects of the regimen (other than alopecia) to ≤ Grade 1 or baseline. * Participants must have two "index" tumors that meet the following criteria: * Index tumor A (lesion to receive palliative radiation therapy): * is deemed by the treating radiation oncologist to potentially benefit from palliative radiation * is at least 1 cm in longest dimension for lesions not located in the bone, if radiating bone, presence of a bone lesion is sufficient. * Index tumor B (lesion to undergo biopsy): * Is deemed by the treating physician to be amenable to biopsy * Is at least 1 cm in longest dimension. * Participants must be willing to provide at least 2 research biopsies (up to 3 research biopsies) during the conduct of the study. * Note: If a subject is scheduled to have a baseline or on-study tumor biopsy, and the investigator believes that the tumor tissue cannot be obtained safely, then the biopsy may be omitted with approval by the Sponsor-Investigator. The participant may be replaced in order to enroll sufficient number of subjects for biomarker evaluation. * Note: Care should be taken to biopsy the same lesions for research samples. The preference is for the same lesion to be biopsied at all time points. If a lesion is no longer amenable for a research biopsy (for examples: due to a decrease in size, becomes inaccessible, is not safe/feasible for a biopsy), then an alternative lesion may be utilized with approval by the Sponsor-Investigator. Index tumor B (lesion to undergo biopsy) must not have received palliative radiation therapy during the study. * Participants must be willing to provide at least 2 collections of fresh research biopsies (up to 3 fresh research biopsies) during the conduct of this study. * Research biopsy #1 (baseline, mandatory). Archival tissue obtained since completion of last therapy may be used. * Research biopsy #2 (cycle 1 days 9-14, after treatment with INCB081776 but prior to pembrolizumab, mandatory) * Research biopsy #3 (cycle 1 day 37-56, after treatment with INCB081776, pembrolizumab and palliative RT). For participants who had baseline archival tissue collected (no baseline research biopsy was obtained), this fresh core biopsy is mandatory. For participants who underwent a fresh core research biopsy at baseline, this biopsy is optional. * Note: If a participant is scheduled to have an on-study tumor biopsy, and the investigator believes that the tumor tissue cannot be obtained safely, then the biopsy may be omitted after discussion with the Sponsor-Investigator. The participant may be replaced in order to enroll sufficient number of subjects for biomarker evaluation. * Note: Care should be taken to biopsy the same lesion for the on-treatment samples Exclusion Criteria: * Subjects with significant intercurrent illnesses per physician discretion. * Subjects with a diagnosed auto-immune disease requiring systemic treatment with immunosuppressants. * Subjects with known genetic conditions causing pre-disposition to RT toxicity (i.e: Li-Fraumeni, ATM deficiency, active scleroderma, etc.). * Subjects with known retinal or ophthalmologic disorders or conditions. Subjects with macular degeneration, proliferative diabetic retinopathy or diabetic retinopathy with macular edema, retinal vein occlusions, uveitis, central serous retinopathy, leukemic retinopathy, inherited retinal degenerations, known family history of inherited retinal degenerations, and subjects at risk for angle closure glaucoma from pupillary dilation are ineligible. Subjects with other clinically significant abnormalities identified during ophthalmic screening examinations that may confound ocular monitoring are ineligible.