The fidelity of signal transduction requires the binding of regulatory molecules to their cognate targets. However, the crowded cell interior risks off-target interactions between proteins that are functionally unrelated. How such off-target interactions impact fitness is not generally known. Here, we use Saccharomyces cerevisiae to inducibly express tyrosine kinases. Because yeast lacks bona fide tyrosine kinases, the resulting tyrosine phosphorylation is biologically spurious. We engineered 44 yeast strains each expressing a tyrosine kinase, and quantitatively analysed their phosphoproteomes. This analysis resulted in ~30,000 phosphosites mapping to ~3500 proteins. The number of spurious pY sites generated correlates strongly with decreased growth, and we predict over 1000 pY events to be deleterious. However, we also find that many of the spurious pY sites have a negligible effect on fitness, possibly because of their low stoichiometry. This result is consistent with our evolutionary analyses demonstrating a lack of phosphotyrosine counter-selection in species with tyrosine kinases. Our results suggest that, alongside the risk for toxicity, the cell can tolerate a large degree of non-functional crosstalk as interaction networks evolve.