Erlotinib Hydrochloride and Cetuximab in Treating Patients With Advanced Gastrointestinal Cancer, Head and Neck Cancer, Non-Small Cell Lung Cancer, or Colorectal Cancer

PRIMARY OBJECTIVES: I. To identify the maximum tolerated dose (MTD). II. To identify the recommended dose (RD) for phase II of erlotinib (erlotinib hydrochloride) in combination with cetuximab in patients (pts) with incurable gastrointestinal, head and neck, or non-small cell lung cancers that are Kirsten rat sarcoma viral oncogene homolog (KRAS) wild type. SECONDARY OBJECTIVES: I. To identify dose-limiting toxicities (DLT). II. To perform skin and tumor biopsies to analyze molecular inhibition of the epidermal growth factor receptor (EGFR) signaling pathway, defined as a \>= 75% inhibition of phosphorylation of the epidermal growth factor (EGF) receptor or of its downstream effectors tumor protein (p)44/42 mitogen-activated protein kinase (MAPK) or protein kinase B (Akt) or as a \>= 25% decrease of marker of proliferation Ki-67 (Ki67) from baseline in either skin or tumor tissue in the majority of patients. III. To identify the optimal biological dose (OBD). IV. To describe any antitumor effect observed. OUTLINE: This is a phase I, dose-escalation study of erlotinib hydrochloride. Patients receive cetuximab intravenously (IV) over 1-2 hours on days 1, 8, and 15 and erlotinib hydrochloride orally (PO) once daily (QD) on days 8-21. Treatment repeats every 21 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed for 4 weeks.