Additional Study Information: The purpose of this study is to test the good and bad effects of the combined treatment, using the drugs cetuximab and avelumab as well as avelumab by itself. Avelumab is a drug that works by triggering the immune system so it can try to attack the cancer again. Avelumab works in a similar way to cemiplimab, which is the usual drug for treatment of your cancer. Cetuximab can also boost the immune system while working against the cancer in other ways. We know that cetuximab has shrunk or stabilized cSCC in other patients. The study is specifically looking to determine whether the combination of the study drugs avelumab and cetuximab is better than avelumab alone. Both avelumab and cetuximab have already been approved by the FDA to treat other cancers. We don't know if the combination of cetuximab and avelumab works to treat cancer in people, but it has shrunk several types of tumors in animals. There will be about 59 people taking part in this study.