  We construct an expression for a general lepton flavour universality (LFU)
ratio, $R_{X}$, in $b\to s l^+ l^-$ decays in terms of a series of hadronic
quantities which can be treated as nuisance parameters. This expression allows
to include any LFU ratio in global fits of $b\to s l^+ l^-$ short-distance
parameters, even in the absence of a precise knowledge of the corresponding
hadronic structure. The absence of sizeable LFU violation and the approximate
left-handed structure of the Standard Model amplitude imply that only a very
limited set of hadronic parameters hamper the sensitivity of $R_X$ to a
possible LFU violation of short-distance origin. A global $b\to s l^+ l^-$
combination is performed including the measurement of $R_{pK}$ for the first
time, resulting in a significance of new physics of $4.2\,\sigma$. In light of
this, we evaluate the impact on the global significance of new physics using a
set of experimentally promising non-exclusive $R_X$ measurements that LHCb can
perform, and find that they can significantly increase the discovery potential
of the experiment.
