ABSTRACT The Hippo tumour suppressor pathway controls transcription by regulating nuclear abundance of YAP and TAZ, which activate transcription with the TEAD1-TEAD4 DNA-binding proteins. Recently, several small-molecule inhibitors of YAP and TEADs have been reported, with some now entering clinical trials for different cancers. Here, we investigated the cellular response to TEAD palmitoylation inhibitors, using a combination of genomic and genetic strategies. Genome-wide CRISPR/Cas9 screens identified genes that modulate the cellular response to TEAD inhibition, including members of the Hippo, MAPK and JAK-STAT signaling pathways. By exploring gene expression programs of mutant cells, we found that MAPK pathway hyperactivation confers resistance to TEAD inhibition by reinstating expression of a subset of YAP/TEAD target genes. Consistent with this, combined inhibition of TEAD and the MAPK protein MEK, synergistically blocked proliferation of several mesothelioma and lung cancer cell lines and more potently reduced the growth of patient-derived lung cancers in vivo. Collectively, we reveal mechanisms by which cells can overcome small-molecule inhibition of TEADs and potential strategies to enhance the anti-tumor activity of emerging Hippo pathway targeted therapies.