  Upcoming experiments will improve the reach for the lepton flavour violating
(LFV) processes $\mu \to e \gamma$, $\mu \to e \bar{e} e$ and $\mu A \to e A$
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 involving twelve Wilson
coefficients that can in principle all be determined by experimental
measurements. 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 $\mu \to e$ experiments have the ability to rule them
out.
