This is an open-label, safety study of cetuximab and differing dose levels of dasatinib in adult patients with advanced solid malignancies. Cetuximab will be administered as an intravenous infusion weekly. Dasatinib will be taken orally, once a day, on a continuous schedule at differing dose levels. The primary objective of this study is to determine the toxicities and the maximum tolerated doses of dasatinib when combined with cetuximab for the treatment of advanced solid tumors.