Participants with recurrent or metastatic squamous cell carcinoma of the head and neck (SCCHN) who had prior immune checkpoint inhibitor and platinum-based chemotherapy treatment will be randomized in a 2:1 ratio to monalizumab and cetuximab or placebo and cetuximab. Efficacy and safety assessments will be performed periodically from the time of enrollment and throughout the study. Participants in all arms will continue therapy until progression, unacceptable toxicity, withdrawal of consent, or another discontinuation criterion is met. All Participants will be followed for survival after progression is confirmed.