This phase III trial compares the effect of decreased number of radiation (ultra-hypofractionated) treatments to the usual radiation number of treatments (hypofractionation) with standard of care chemotherapy, with cisplatin, gemcitabine or mitomycin and 5-fluorouracil for the treatment of patients with muscle invasive bladder cancer. Hypofractionated radiation therapy delivers higher doses of radiation therapy over a short period of time. Ultra-hypofractionated radiation therapy delivers radiation over an even shorter period of time than hypofractionated radiation therapy. Cisplatin is in a class of medications known as platinum-containing compounds. It works by killing, stopping or slowing the growth of tumor cells. Gemcitabine is a chemotherapy drug that blocks the cells from making DNA and may kill tumor cells. Chemotherapy drugs, such as mitomycin-C and 5-fluorouracil (5-FU), 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. Giving ultra-hypofractionated radiation may be equally effective as hypofractionated therapy for patients with muscle invasive bladder cancer.

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.