  In recent years, intriguing hints for the violation of Lepton Flavour
Universality (LFU) have been accumulated in semileptonic $B$ decays, both in
the neutral-current transitions $b\to s\ell^+\ell^-$ (i.e., $R_K$ and
$R_{K^*}$) and the charged-current transitions $b\to c\ell^-\bar\nu_\ell$
(i.e., $R_D$, $R_{D^*}$ and $R_{J/\psi}$). LHCb has reported deviations from
the Standard Model (SM) expectations in $b\to s\mu^+\mu^-$ processes as well as
in the ratios $R_K$ and $R_{K^*}$, which together point at New Physics (NP)
affecting muons with a high significance. Furthermore, hints for LFU violation
in $R_{D^{(*)}}$ and $R_{J/\psi}$ point at large deviations from the SM in
processes involving tau leptons. Together, these hints for NP motivate the
possibility of huge LFU-violating effects in $b\to s\tau^+\tau^-$ transitions.
In this article we predict the branching ratios of $B\to K\tau^+\tau^-$, $B\to
K^{*}\tau^+\tau^-$ and $B_s\to \phi \tau^+\tau^-$ taking into account NP
effects in the Wilson coefficients $C_{9(')}^{\tau\tau}$ and
$C_{10(')}^{\tau\tau}$. Assuming a common NP explanation of $R_{D^{}}$ ,
$R_{D^{(*)}}$ and $R_{J/\psi}$, we show that a very large enhancement of $b\to
s\tau^+\tau^-$ processes, of around three orders of magnitude compared to the
SM, can be expected under fairly general assumptions. We find that the
branching ratios of $B_s\to \tau^+\tau^-$, $B_s\to \phi \tau^+\tau^-$ and $B\to
K^{(*)}\tau^+\tau^-$ under these assumptions are in the observable range for
LHCb and Belle II.
