Although epidermal growth factor receptor (EGFR; also called ErbB1) and its relatives initiate one of the most well-studied signalling networks, there is not yet a genome-wide view of even the earliest step in this pathway: recruitment of proteins to the activated receptors. Here we use protein microarrays comprising virtually every Src homology 2 (SH2) and phosphotyrosine binding (PTB) domain encoded in the human genome to measure the equilibrium dissociation constant of each domain for 61 peptides representing physiological sites of tyrosine phosphorylation on the four ErbB receptors. This involved 77,592 independent biochemical measurements and provided a quantitative protein interaction network that reveals many new interactions, including ones that fall outside of our current view of domain selectivity. By slicing through the network at different affinity thresholds, we found surprising differences between the receptors. Most notably, EGFR and ErbB2 become markedly more promiscuous as the threshold is lowered, whereas ErbB3 does not. Because EGFR and ErbB2 are overexpressed in many human cancers, our results suggest that the extent to which promiscuity changes with protein concentration may contribute to the oncogenic potential of receptor tyrosine kinases, and perhaps other signalling proteins as well.