Rare semileptonic b→sℓ+ℓ− transitions provide some of the most promising framework to search for new physics effects. Recent analyses of these decays have indicated an anomalous behaviour in measurements of angular distributions of the decay B0→K∗μ+μ− 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 B¯0→K¯∗0μ+μ− and B¯0→K¯∗0e+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 non-perturbative 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 datasets.