Study Evaluating the Efficacy of Niraparib and Dostarlimab (TSR-042) in Recurrent/Metastatic HNSCC

Inclusion Criteria: * Histologically, cytologically, or radiographically confirmed recurrent or metastatic non cutaneous HNSCC for which there are no surgical or radiation curative options. * ECOG performance status ≤2 * Patients must be able to swallow pills Exclusion Criteria: * Nasopharyngeal and salivary gland tumors * Patients who have not recovered from adverse events due to prior anti-cancer therapy with the exception of alopecia * Prior exposure to both immunotherapy drugs (PD-1, PDL-1, CTLA-4 inhibitors) and PARP inhibitors. Single exposure to either immunotherapy or PARP inhibitors is allowable. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to niraparib or dostarlimab. * Patients with uncontrolled intercurrent illness. * Requirement of any use of steroids greater than the equivalent of 10mg prednisone daily is not allowed.