This phase II/III trial compares the addition of nivolumab to the usual treatment of paclitaxel and ramucirumab to paclitaxel and ramucirumab alone in treating patients with gastric or esophageal adenocarcinoma that that may have spread from where it first started to nearby tissue, lymph nodes, or distant parts of the body (advanced). A monoclonal antibody is a type of protein that can bind to certain targets in the body, such as molecules that cause the body to make an immune response (antigens). Immunotherapy with monoclonal antibodies, such as nivolumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Ramucirumab is a monoclonal antibody that may prevent the growth of new blood vessels that tumors need to grow. Paclitaxel is in a class of medications called antimicrotubule agents. It stops cancer cells from growing and dividing and may kill them. Adding nivolumab to ramucirumab and paclitaxel may work better to treat patients with advanced stomach or esophageal cancer.

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.