This is a phase Ib open label, expansion study of CUDC-101 in patients with advanced head and neck, gastric, breast, liver, and non-small cell lung cancer tumors. CUDC-101 is a multi-targeted agent designed to inhibit epidermal growth factor receptor (EGFR), human epidermal growth factor receptor Type 2 (Her2) and histone deacetylase (HDAC). The study is designed to compare the safety and tolerability of CUDC-101 when administered at the maximum tolerated dose on either a 5 days/week schedule or a 3 days/week schedule.