Résumé
Upcoming $\mu\leftrightarrow e$ experiments promise exceptional sensitivity to a few key processes, reaching branching ratios $\lesssim 10^{-16}$ for $\mu\to e$ conversion on aluminium. Upcoming $\tau\leftrightarrow l$ searches will probe many processes down to $BR\sim 10^{-9}$. In an EFT context, we show that some combinations of $\mu\to\tau$ and $\tau\to e$ interactions could induce detectable $\mu\to e$ while remaining out of reach to $\tau\leftrightarrow l$ searches.