 This phase I trial studies the side effects and best dose of entolimod in treating patients with stage III-IV or recurrent head and neck cancer. Biological therapies, such as entolimod, may stimulate the immune system in different ways and stop tumor cells from growing. Entolimod may also prevent side effects caused by chemotherapy with cisplatin and radiation therapy. Radiation therapy uses high-energy x-rays to kill tumor cells. Drugs used in chemotherapy, such as cisplatin, work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Giving entolimod together with cisplatin and radiation therapy may kill more tumor cells 