  Rare semileptonic $b \to s \ell^+ \ell^-$ transitions provide some of the
most promising frameworks to search for new physics effects. Recent analyses of
these decays have indicated an anomalous behaviour in measurements of angular
distributions of the decay $B^0\to K^*\mu^+\mu^-$ and
lepton-flavour-universality observables. Unambiguously establishing if these
deviations have a common nature is of paramount importance in order to
understand the observed pattern. We propose a novel approach to independently
and complementary probe this hypothesis by performing a simultaneous amplitude
analysis of $\bar{B}^0 \to \bar{K}^{*0} \mu^+\mu^-$ and $\bar{B}^0 \to
\bar{K}^{*0} e^+e^-$ decays. This method enables the direct determination of
observables that encode potential non-equal couplings of muons and electrons,
and are found to be insensitive to nonperturbative QCD effects. If current
hints of new physics are confirmed, our approach could allow an early discovery
of physics beyond the standard model with LHCb run II data sets.
