You can participate in this study if:

• Participants must have histologically documented squamous cell head and neck carcinoma that meets one of the following criteria; was metastatic at diagnosis, persisted, metastasized or recurred following definitive treatment, or recurred locally and participant has either a contraindication to surgical treatment of lesions (i.e., complete resection is not possible or not expected to be clinically beneficial or resection confers significant functional concerns) or has refused surgical or radiation treatment.
• Participants must have measurable disease documented by CT or MRI. Measurable disease must be assessed within 28 days prior to registration and non-measurable disease must be assessed within 42 days prior to registration.
• Participants must have received prior therapy with a Programmed death ligand 1 (PD-(L)1) inhibitor or PD-1 inhibitor for treatment of head and neck cancer (in any setting).
• Participants must be 18 years old or older at the time of registration.
• Participants must have adequate organ and marrow function within 28 days prior to registration
• Participants must have a calculated creatinine clearance greater than or equal to 45 mL/min
• Participants with known human immunodeficiency virus (HIV)-infection must be on effective anti-retroviral therapy and have undetectable viral load test on the most recent test results obtained within 6 months prior to registration.
• Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. Participants must have an undetectable HCV viral load test on the most recent test results obtained within 6 months prior to registration, if indicated.
• Participants must be offered the opportunity to participate in specimen banking. With participant consent, specimens must be collected and submitted via the SWOG Specimen Tracking System.

You cannot participate in this study if:

• Participants must not have received more than two prior systemic therapy regimens for recurrent and/or metastatic disease.
• Participants must not have had prior anti-cancer therapy within 14 days of registration.
• Participants must not have received treatment with a platinum or taxane agent as part of a prior treatment for recurrent or metastatic disease.
• Participants must not have had prior treatment with cetuximab or another Epidermal Growth Factor Receptor (EGFR) inhibitor in the locally recurrent advanced unresectable or metastatic setting.
• Participants must not have known hypersensitivity and/or contraindication to carboplatin or paclitaxel in the opinion of the treating investigator.
• Participants must not have active cardiovascular disease
• Participants must not have an uncontrolled illness
• Participants must not have had major surgery (excluding placement of vascular access, percutaneous feeding tube replacement, tracheostomy, or tumor biopsy) or had significant traumatic injury within 28 days prior to registration.
• Participants must not have other clinically active infectious liver diseases.
• Participants must not have a concurrent malignancy whose natural history or treatment (in the opinion of the treating investigator) has the potential to interfere with the safety or efficacy assessment of the investigational regimen.
• Participants must not be pregnant or nursing