  We investigate the possibility of indirectly constraining the $B^{+}\to
K^{+}\tau^+\tau^-$ decay rate using precise data on the $B^{+}\to
K^{+}\mu^+\mu^-$ dimuon spectrum. To this end, we estimate the distortion of
the spectrum induced by the $B^{+}\to K^{+}\tau^+\tau^-\to K^{+} \mu^+\mu^-$
re-scattering process, and propose a method to simultaneously constrain this
(non-standard) contribution and the long-distance effects associated to
hadronic intermediate states. The latter are constrained using the analytic
properties of the amplitude combined with data and perturbative calculations.
Finally, we estimate the sensitivity expected at the LHCb experiment with
present and future datasets. We find that constraints on the branching fraction
of $O(10^{-3})$, competitive with current direct bounds, can be achieved with
the current dataset, while bounds of $O(10^{-4})$ could be obtained with the
LHCb upgrade-II luminosity.
