  As a result of the helicity suppression effect, within the Standard Model the
rare decay channel $B_s \to e^+ e^-$ has a decay probability which is five
orders of magnitude below current experimental limits. Thus, any observation of
this channel within the current or forthcoming experiments will give
unambiguous evidence of Physics Beyond the Standard Model. In this work, we
present for the first time a New Physics scenario in which the branching
fraction $\bar{\mathcal{B}}r(B_s \to e^+ e^-)$ is enhanced up to values which
saturate the current experimental bounds. More concretely, we study the general
Two-Higgs-Doublet Model (2HDM) with a pseudoscalar coupling to electrons
unsuppressed by the electron mass. Furthermore, we demonstrate how this
scenario can arise from a UV-complete theory of quark-lepton unification that
can live at a low scale. This latter step allows us to establish correlations
between $B_s \to e^+ e^-$ and the lepton-flavour-violating decays $\tau^{-}\to
\mu^{-}e^+ e^-$ and $\tau\to \mu \gamma$.
