This open-label, multicenter study will evaluate the safety, tolerability, and pharmacokinetics of MEHD7945A in combination with chemotherapy (either cisplatin plus 5-FU or carboplatin plus paclitaxel) in participants with previously untreated R/M SCCHN. There are two stages for each arm in this study: a Dose-limiting Toxicity (DLT)-evaluation stage (Stage I) and a cohort-expansion stage (Stage II). In Stage I, DLTs will be assessed during a DLT Assessment Window of 21 days (i.e., Cycle 1 Day 1 through Cycle 1 Day 21) for both arms. In Stage II, participants will be enrolled to further characterize the safety, pharmacokinetics, and anti-tumor activity of MEHD7945A in combination with cisplatin + 5-FU or carboplatin + paclitaxel at the identified recommended Phase II dose.

Inclusion Criteria:

• Histologically confirmed R/M SCCHN of mucosal origin (e.g., oral cavity, oropharynx, hypopharynx, larynx) that is not amenable to further curative local therapy (e.g., surgery, radiation including re-irradiation) (1L R/M)
• Participants with unknown primary SCCHN presumed to be of head and neck mucosal origin are eligible if they meet all other entry criteria
• For participants who present with de novo metastatic disease, no prior systemic chemotherapy is allowed
• For participants with recurrent SCCHN, prior systemic therapy is allowed if it was given as part of induction or definitive therapy. If participants have received prior combined chemo-radiation therapy, they must be off therapy for at least 3 months
• Consent to provide archival tumor tissue for biomarker testing
• Life expectancy greater than or equal to (>/=) 12 weeks
• Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2
• Disease that is measurable per modified RECIST v1.1
• Adequate bone marrow and organ function

Exclusion Criteria:

• Nasopharyngeal cancer
• Prior treatment with an investigational or approved agent for the purpose of inhibiting human epidermal growth factor receptor (HER) family members. This includes, but is not limited to, cetuximab, panitumumab, erlotinib, gefitinib, and lapatinib
• Prior treatment with an epidermal growth factor receptor (EGFR) inhibitor is allowed if it was administered as part of definitive therapy for locally advanced disease and completed/terminated >/= 3 months before study enrollment
• Major surgical procedure within 4 weeks prior to Day 1
• Leptomeningeal disease as the only manifestation of the current malignancy
• Active infection requiring antibiotics
• Active autoimmune disease that is not controlled by nonsteroidal anti-inflammatory drugs (NSAIDs)
• Symptomatic hypercalcemia requiring continued use of bisphosphonate therapy
• Current severe, uncontrolled systemic disease
• History of cardiac heart failure of New York Heart Association Class II or greater or serious cardiac arrhythmia requiring treatment (except for atrial fibrillation and paroxysmal supraventricular tachycardia)
• History of myocardial infarction within 6 months prior to 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 bleeding diathesis or coagulopathy other than that due to anticoagulation therapy
• Clinically significant gastrointestinal (GI) bleeding within 6 months prior to Cycle 1, Day 1
• History of interstitial lung disease (ILD)
• History of severe (Grade 3 or 4) allergic or hypersensitivity reaction to therapeutic antibodies that required discontinuation of therapy
• Known human immunodeficiency virus (HIV) infection
• Untreated/active central nervous system (CNS) metastases (progressing or requiring anticonvulsants or corticosteroids for symptomatic control)
• Pregnant or lactating women
• Malignancies other than SCCHN within 5 years prior to enrollment, with the exception of adequately treated basal or squamous cell skin cancer and carcinoma in situ of the cervix or skin (e.g., melanoma in situ) or indolent prostate cancer