This is a phase 3 open-label, randomized, controlled, multicenter study to compare petosemtamab vs investigator's choice monotherapy in HNSCC patients for the second- and third-line treatment of incurable metastatic/recurrent disease. HNSCC patients must have progressive disease (PD) on or after anti-PD-1 therapy and platinum-containing therapy. Patients treated with platinum-containing therapy only in the adjuvant setting, or in the context of multimodal therapy for locally advanced disease, should have PD within 6 months of the last dose of platinum-containing therapy.