Recombinant EphB4-HSA Fusion Protein and Pembrolizumab, MK-3475

This phase IIa trial studies how well recombinant EphB4-HSA fusion protein and pembrolizumab work in treating patients with non-small cell lung cancer that has spread to other places in the body or head and neck squamous cell cancer that has come back or spread to other places in the body. Recombinant EphB4-HSA fusion protein may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Monoclonal antibodies, such as pembrolizumab, may interfere with the ability of cancer cells to grow and spread. Giving recombinant EphB4-HSA fusion protein and pembrolizumab may work better in treating patients with non-small cell lung or head and neck squamous cell cancer.