In this phase II clinical trial of personalized immunotherapy in advanced head and neck cancers, gene expression of LAG-3 and CTLA-4 by RNAseq is determined to select the appropriate agent (ipilimumab or relatlimab) to add to nivolumab in patients with R/M HNSCC who have failed prior immunotherapy with anti-PD-1 or PD-L1 mAb therapy. This evidence concerns the gene PDCD1 and head and neck squamous cell carcinoma.