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.

Inclusion Criteria:

• Life expectancy greater than or equal to (>/=) 12 weeks
• Availability and willingness to provide sufficient tumor tissue sample for testing
• Dose-escalation stage: Participants with histologically documented incurable, locally advanced, or metastatic epithelial malignancy that has progressed despite standard therapy or for which no standard therapy exists
• Expansion stage: Participants with one of the following epithelial, histologically-documented, incurable, locally advanced, or metastatic tumor that has progressed despite standard therapy or for which no standard therapy exists: CRC, NSCLC, HNSCC, or pancreatic cancer
• Use of an effective means of contraception (e.g., abstinence, hormonal or double barrier method, surgically sterilized partner) for men and women of childbearing potential while enrolled in the study

Exclusion Criteria:

• Less than (<) 4 weeks since the last anti-tumor therapy prior to Day 1 of study treatment
• Major surgical procedure within 4 weeks prior to Cycle 1, Day 1
• Leptomeningeal disease as the only manifestation of the current malignancy
• Active infection requiring IV antibiotics
• Active autoimmune disease that is not controlled by nonsteroidal anti-inflammatory drugs
• Symptomatic hypercalcemia requiring continued use of bisphosphonate therapy
• Current severe, uncontrolled systemic disease
• History of cardiac heart failure of any New York Heart Association criteria or serious cardiac arrhythmia requiring treatment
• History of myocardial infarction within 6 months before Cycle 1, Day 1, or history of unstable angina
• Clinically significant history of liver disease, including viral or other hepatitis, current alcohol abuse, or cirrhosis
• History of interstitial lung disease
• History of severe allergic or hypersensitivity reaction to other therapeutic antibodies that required discontinuation of therapy
• Known human immunodeficiency virus (HIV) infection
• Primary central nervous system (CNS) malignancy or untreated/active CNS metastases
• Significant traumatic injury within 4 weeks before Cycle 1, Day 1
• Pregnancy or lactation