This phase III trial compares pembrolizumab with radiation therapy to pembrolizumab without radiation therapy (standard therapy) given after pembrolizumab plus chemotherapy for the treatment of patients with squamous cell carcinoma of the head and neck that has spread from where it first started (primary site) to other places in the body (metastatic). Pembrolizumab is a type of immunotherapy that stimulates the body's immune system to fight cancer cells. Pembrolizumab targets and blocks a protein called PD-1 on the surface of certain immune cells called T-cells. Blocking PD-1 triggers the T-cells to find and kill cancer cells. Radiation therapy uses high-powered rays to kill cancer cells. Giving radiation with pembrolizumab may be more effective at treating patients with metastatic head and neck cancer than the standard therapy of giving pembrolizumab alone.

This study is being done to answer the following questions: Is the chance of rectal cancer responding the same if chemotherapy alone is given before limited surgery compared to chemotherapy and radiation therapy given together before limited surgery? If radiation therapy is not given, is quality of life better?