The accumulation of genetic and epigenetic alterations in cancer cells rewires cellular signalling pathways through changes in the patterns of protein-protein interactions (PPIs). Understanding these patterns may facilitate the design of tailored cancer therapies. Here, we show that single-molecule pull-down and co-immunoprecipitation techniques can be used to characterize signalling complexes of the human epidermal growth-factor receptor (HER) family in specific cancers. By analysing cancer-specific signalling phenotypes, including post-translational modifications and PPIs with downstream interactions, we found that activating mutations of the epidermal growth-factor receptor (EGFR) gene led to the formation of large protein complexes surrounding mutant EGFR proteins and to a reduction in the dependency of mutant EGFR signalling on phosphotyrosine residues, and that the strength of HER-family PPIs is correlated with the strength of the dependence of breast and lung adenocarcinoma cells on HER-family signalling pathways. Furthermore, using co-immunoprecipitation profiling to screen for EGFR-dependent cancers, we identified non-small-cell lung cancers that respond to an EGFR-targeted inhibitor. Our approach might help predict responses to targeted cancer therapies, particularly for cancers that lack actionable genomic mutations.