The integrated stress response is a signaling network comprised of four branches, each of which senses different cellular stressors, converging on the phosphorylation of eIF2α to depress global translation and initiate recovery. One of these branches is composed of GCN2, which senses cellular amino acid insufficiency and participates in the maintenance of amino acid homeostasis. Previous studies have shown that GCN2 is a viable cancer target when amino acid stress is provoked by inhibiting an additional target. In this light, we screened a combination of drugs to identify biologically active compounds which synergize with the GCN2 inhibitor TAP20. First, a panel of 25 compounds was assayed in six cancer cell lines for drug sensitivity. Each compound was then combined with TAP20 at concentrations below their IC50, and the impact on cell growth was assessed. Selected strongly synergistic combinations were further characterised using synergy analyses and matrix-dependent invasion assays. Inhibitors of proteostasis, of the MEK-ERK pathway and pan-CDK inhibitors flavopiridol and seliciclib were found to potently synergize with TAP20 in two of the tested cell lines. Among their common CDK targets is CDK7, which was selectively targeted with THZ-1 and found to synergize with TAP20. Finally, these combinations were found to be partially synergistic when assessed using matrix-dependent invasion assays. However, we found that TAP20 alone was sufficient to restrict invasion at concentrations well below its growth-inhibitory IC50. We conclude that GCN2 can be targeted for treating cancers by polytherapy or even monotherapy.