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Abstract Upcoming experiments will improve the reach for the lepton flavour violating (LFV) processes μ → eγ, μ → e e ¯ e $$ e\overline{e}e $$ and μA → eA by orders of magnitude. We investigate whether this upcoming data could rule out some popular TeV-scale LFV models (the type II seesaw, the inverse seesaw and a scalar leptoquark) using a bottom-up EFT approach. We take the data to be the twelve Wilson coefficients that experiments can constrain and in principle determine independently. In this 12-dimensional coefficient space, each model can only predict points in a specific subspace; for instance, flavour change involving singlet electrons is suppressed in the seesaw models, and the leptoquark induces negligible coefficients for 4-lepton scalar operators. Using the fact that none of these models can populate the whole region accessible to upcoming experiments, we show that μ → e experiments have the ability to rule them out.