This phase I/II trial tests the safety and efficacy of split-course adaptive radiation therapy in combination with immunotherapy with or without chemotherapy for the treatment of patients with stage IV lung cancer or lung cancer that that has spread to nearby tissue or lymph nodes (locally advanced). Radiation therapy is a standard cancer treatment that uses high energy rays to kill cancer cells and shrink tumors. Split-course adaptive radiation therapy uses patient disease response to alter the intensity of the radiation therapy. Immunotherapy with monoclonal antibodies such as pembrolizumab, ipilimumab or nivolumab may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Chemotherapy drugs like carboplatin, pemetrexed, and paclitaxel work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving split-course adaptive radiation therapy with standard treatments like immunotherapy and chemotherapy may be more effective at treating stage IV or locally advanced lung cancer than giving them alone.

This phase III trial compares the effect of the combination of fluorouracil, oxaliplatin, and leucovorin calcium (FOLFOX) or capecitabine and oxaliplatin (CAPOX) followed by limited surgery with transanal endoscopic surgery (TES) versus chemoradiation followed by TES for the treatment of early stage rectal cancer. The usual approach for patients who are not in a study is surgery to remove the rectum or treatment with chemotherapy and radiation therapy, followed by surgery. Fluorouracil stops cells from making deoxyribonucleic acid (DNA) and it may kill tumor cells. Leucovorin is in a class of medications called folic acid analogs. When used with fluorouracil, it enhances the effects of this chemotherapy drug. Oxaliplatin is in a class of medications called platinum-containing antineoplastic agents. It damages the cells DNA and may kill cancer cells. CAPOX is a combination of two drugs (capecitabine and oxaliplatin) and used as standard chemotherapy in treatment of rectal cancer. CAPOX works by damaging the DNA in tumor cells, and may cause the cells to stop growing and die. Radiation therapy uses high energy x-rays, particles, or radioactive seeds to kill tumor cells and shrink tumors. This study will help researchers find out if chemotherapy with FOLFOX or CAPOX prior to surgery works better, the same, or worse than the usual approach and improves the quality of life in patients with early rectal cancer.