A Study of RO5479599 Alone or in Combination With Cetuximab or Erlotinib in Participants With Metastatic and/or Locally Advanced Malignant Human Epidermal Growth Factor Receptor (HER3) Expressing Solid Tumors of Epithelial Cell Origin

Inclusion Criteria:

All Parts (A, B and C)

* European Cooperative Oncology Group (ECOG) performance status 0-2
* Histologically confirmed metastatic and/or locally advanced malignant HER3-expressing solid tumors of epithelial origin
* Availability of tissue and willingness to perform fresh pretreatment biopsies
* Participants for whom no standard therapy exists
* All acute toxic effects of any prior radiotherapy, chemotherapy or surgical procedure must have resolved to Grade less than or equal to (\</= 1), except for alopecia and Grade 2 peripheral neuropathy
* Adequate hematological, renal and liver function
* Participants with Gilbert's syndrome will be eligible for the study

Part B extension cohort: In addition to the above inclusion criteria, participants will be eligible if they have metastatic and/or locally advanced non-small cell lung cancer or squamous cell carcinoma of the head and neck or colorectal cancer (wild type with positive epidermal growth factor receptor \[EGFR\] expression)

Part C extension cohort: In addition to the above inclusion criteria, participants will be eligible only if they have metastatic and/or locally advanced squamous non-small cell lung cancer

Exclusion Criteria:

* Known or clinically suspected central nervous system (CNS) primary tumors or metastases including leptomeningeal metastases. History or clinical evidence of CNS metastases unless they have been previously treated, are asymptomatic and have had no requirement for steroids or enzyme-inducing anticonvulsants in the last 14 days
* Evidence of significant uncontrolled concomitant diseases or disorders
* Active or uncontrolled infections
* Known Human immuno deficiency virus (HIV) infection
* Therapy with antibody or immunotherapy concurrently or within 14 days prior to first dose of study drug
* Regular immunosuppressive therapy
* Concurrent high dose of systemic corticosteroids (greater than (\>) 20 milligrams per day \[mg/day\] dexamethasone or equivalent for \> 7 consecutive days)