TLR8 Agonist VTX-2337 and Cetuximab in Treating Patients With Locally Advanced, Recurrent, or Metastatic Squamous Cell Cancer of Head and Neck

Inclusion Criteria: * Patients with a histological or cytopathological confirmed diagnosis of squamous cell carcinoma of the head and neck region that is: * Locally advanced/recurrent and no longer amenable to local surgical or radiation therapy and/or * Has evidence of metastatic disease * Patients may have been previously treated with systemic therapy but are otherwise deemed currently platinum-refractory, or would be deemed inappropriate or intolerant to platinum-based chemotherapy * Patients must have completed definitive chemotherapy and/or radiation therapy \>= 3 months prior to study entry * Prior therapy with agents targeting/blocking the epidermal growth factor receptor (e.g. cetuximab and erlotinib) is allowable * Performance Status: Eastern Cooperative Oncology Group (ECOG) 0 - 2 * Expected life expectancy of at least 12 weeks, as assessed by the Investigator * Ability and willingness to comply with the study's visit and assessment schedule and to provide voluntary written informed consent * Absolute neutrophil count (ANC) \>= 1,500 cells/μL * Platelet count \>= 75,000 cells/μL * Hemoglobin \>= 8.0 g/dL * Creatinine =\< 2.0 mg/dL * Total bilirubin =\< 2.0 x upper limit of normal (ULN) * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]), serum glutamic pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 2.5 x ULN * For patients with liver metastases, AST, ALT \< 5x ULN is acceptable * Willingness to use a me…