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 phase III trial studies how well active surveillance help doctors to monitor subjects with low risk germ cell tumors for recurrence after their tumor is removed. When the germ cell tumors has spread outside of the organ in which it developed, it is considered metastatic. Drugs used in chemotherapy, such as bleomycin, carboplatin, etoposide, and cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. The trial studies whether carboplatin or cisplatin is the preferred chemotherapy to use in treating metastatic standard risk germ cell tumors.

This phase II trial studies the effect of pembrolizumab alone compared to the usual approach (chemotherapy [cisplatin and carboplatin] plus radiation therapy) after surgery in treating patients with head and neck squamous cell carcinoma that has come back (recurrent) or patients with a second head and neck cancer that is not from metastasis (primary). Radiation therapy uses high energy radiation or protons to kill tumor cells and shrink tumors. Cisplatin is in a class of medications known as platinum-containing compounds. It works by killing, stopping or slowing the growth of cancer cells. Carboplatin is also in a class of medications known as platinum-containing compounds. It works in a way similar to the anticancer drug cisplatin, but may be better tolerated than cisplatin. Carboplatin works by killing, stopping or slowing the growth of cancer cells. Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack the cancer and may interfere with the ability of tumor cells to grow and spread. Giving pembrolizumab alone after surgery may work better than the usual approach in shrinking recurrent or primary head and neck squamous cell carcinoma.