Carboplatin, Paclitaxel, Cetuximab, and Erlotinib Hydrochloride in Treating Patients With Metastatic or Recurrent Head and Neck Squamous Cell Cancer

Criteria: * Histologically confirmed squamous cell carcinoma of the head and neck that is metastatic or recurrent * No prior systemic therapy for metastatic/recurrent disease * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Prior chemotherapy in the induction, organ preservation or adjuvant setting is permitted if it was completed more than 4 months prior to enrollment on the current study * Prior cetuximab is permitted if it was given for no more than 9 doses in combination with radiation therapy or chemoradiation therapy for initial treatment of locally advanced disease * No prior erlotinib, gefitinib or lapatinib therapy is permitted; nor is prior exposure to any investigational EGFR or panErbB reversible or irreversible inhibitor or any prior panitumumab or investigational EGFR-directed monoclonal antibody permitted * Hemoglobin \> 9.0 G/dl * Absolute neutrophil count (ANC) \> 1500 cells/mcl * Creatinine (Cr) \< 1.8 * Total bilirubin =\< the institution's upper limit of normal (ULN), aspartate aminotransferase (AST) and alanine transaminase (ALT) \< 2 X ULN * No chronic active viral infection * No other malignancy within 3 years * No chronic diarrheal condition * Females should not be pregnant or breast feeding because chemotherapy may be harmful to the fetus or the nursing infant; also, the effects of erlotinib and cetuximab on the developing human fetus are unknown * All females of childbearing potential must have a blood test or urine study within 2 weeks prior to randomization to rule out pregnancy * Women of childbearing potential and sexually active males must use an accepted and effective method of contraception while on treatment and for three months after the completion of treatment * Patients must have measurable disease based on Response Evaluation Criteria In Solid Tumors (RECIST); baseline measurements and evaluations must be obtained within \< 4 weeks of randomization; all areas of disease should be recorded and mapped out in order to assess response and uniformity of response to therapy; disease in previously irradiated sites is considered measurable if there has been unequivocal disease progression or biopsy-proven residual carcinoma following radiation therapy; persistent disease without clear-cut progression after radiotherapy can be considered measurable if biopsy-proven at least 8 weeks after completion of radiation therapy * Patients with a prior history of squamous cell or basal carcinoma of the skin or in situ cervical cancer must have been curatively treated; patients with a history of other prior malignancy must have been treated with curative intent and must have remained disease-free for 3 years post diagnosis * No current peripheral neuropathy \> grade 2 at time of randomization * Patients must not have any co-existing condition that would preclude full compliance with the study * Human immunodeficiency virus (HIV) positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with erlotinib * Patients must have no history of allergic reaction to murine proteins * Ability to understand and the willingness to sign a written informed consent * Patients must not be receiving other investigational anti-cancer therapy * Patients with brain metastases are not eligible * Both men and women and members of all races and ethnic groups are eligible for this trial