This study is for patients who have been diagnosed with Head and Neck Squamous Cell Carcinoma (HNSCC). The investigational drug used in this study is Ficlatuzumab. The main goals of this research study is to study the safety and effectiveness of Ficlatuzumab with or without Cetuximab, to determine which strategy will be more effective, as well as to learn the potential side effects of Ficlatuzumab alone or in combination with Cetuximab. It is unknown exactly how long participants can expect to be in the study. Subjects will receive treatment until the drug is no longer effective on their cancer.