Combining Radiation Therapy With Immunotherapy for the Treatment of Metastatic Squamous Cell Carcinoma of the Head and Neck

Inclusion Criteria: * STEP 1 REGISTRATION: * Patient must be \>= 18 years of age * Patient must have biopsy-proven metastatic squamous cell carcinoma, originating in the oral cavity, larynx, oropharynx, or hypopharynx, with active disease present in both the head and neck and distant sites * NOTE: The tumor from an oropharynx primary site must have known p16 status; p16 positive cancer of unknown primary is allowed as well, provided the disease presentation in consistent with a head and neck primary * Patient can have prior surgical resection of a primary cancer in the head and neck at any previous time, however, residual/recurrent disease in the head and neck must be present on baseline imaging * Any effects from prior cancer therapy for other diseases must be fully resolved and not pose a problem for giving the treatment on this trial * Patient must have 4 or fewer metastatic sites prior to starting any treatment, with thoracic nodal disease considered a single site if encompassable in a tolerable radiotherapy hypofractionated field (i.e.,15 fractions or less) * NOTE: Contiguous/adjacent metastases treatable in a single stereotactic field may be considered a single site * NOTE: Patients with additional indeterminate findings such that the total number of metastatic sites would be more than 4 may be enrolled if a non-malignant etiology to these findings is a reasonable consideration * Patient must have Eastern Cooperative Oncology Group (ECOG) performance status 0-1…