  In this letter we propose a strategy for discerning if new physics in the
Wilson coefficient ${\cal C}_{9\mu}$ is dominantly lepton flavour universality
violating or if it contains a sizable lepton flavour universal component
(${\cal C}_9^{\rm U}$). Distinguishing among these two cases, for which the
model independent fit of the related scenarios exhibits similar pulls w.r.t.
the Standard Model, is crucial to advance our understanding of the $B$
anomalies. We first identify the origin of the degeneracy of these two cases
and point out the key observables that can break it. In particular, while the
observables measured so far that test lepton flavour universality exhibit
similar dependencies to all the relevant Wilson coefficients, the forthcoming
measurement of $Q_5=P_{5}^{\prime\mu}-P_{5}^{\prime e}$ is particularly
sensitive to ${\cal C}_{9\mu}-{\cal C}_{9e}$. In fact, if $Q_5$ were found to
be small (i.e. close to its Standard Model value), this would imply a small
${\cal C}_{9\mu}-{\cal C}_{9e}$ but a sizable ${\cal C}_{9}^{\rm U}$, given the
preference of global fits for a large negative new physics contribution in
${\cal C}_{9\mu}$. We discuss the possible origins of ${\cal C}_9^{\rm U}$, in
particular how it could originate from new physics. Here, a promising scenario,
that could even link $b\to s \ell^+\ell^-$ to $R_{D^{(*)}}$, is the one in
which ${\cal C}_9^{\rm U}$ is generated from a tau loop via an off-shell photon
penguin diagram. This setup predicts the branching ratios of
$B_s\to\tau^+\tau^-$ and $B\to K^{(*)}\tau^+\tau^-$ to lie within the reach of
LHCb, CMS and Belle II. Alternatively, in case of a non-observation of these
tauonic processes, we show that the most natural possibility to generate ${\cal
C}_9^{\rm U}$ is a $Z^\prime$ with partially lepton flavour universal
couplings.
