This is a Phase I, multicenter, open-label study of MEHD7945A in participants with incurable, locally advanced, or metastatic epithelial malignancies that have progressed despite standard therapy or for which no standard therapy exists. The study will be conducted in two stages: a dose escalation stage and an expansion stage. The dose-escalation stage is designed to evaluate the safety, tolerability, and PK of MEHD7945A administered (at five dose levels from 1 to 30 milligrams per kilogram [mg/kg]) every 2 week (Q2W). An expansion stage will be initiated after establishment of maximum tolerated dose (MTD) in dose escalation stage. Participants with refractory or recurrent metastatic colorectal cancer (CRC), non-small cell lung cancer (NSCLC), head and neck squamous cell carcinoma (HNSCC), and pancreatic cancer will be enrolled in an expansion stage to better characterize the safety, tolerability, PK and preliminary assessment of the anti-tumor activity of MEHD7945A.