Searching new physics in rare B-meson decays into multiple muons

New heavy vector bosons and light scalars are predicted in a plethora of models of new physics. In particular, in new strongly interacting sectors they play the role of the $\rho$ and $\pi$ mesons in QCD. We show that some of their interactions, for example those required for the explanation of the $B$ anomalies and the $g-2$ of the muon, can be only probed in $B$ meson decays. We highlight new golden channels not yet studied experimentally, including $B^+ \rightarrow K^+(D^+)\mu^+\mu^-\mu^+\mu^-$ and $B^0\rightarrow K^{*0}\mu^+\mu^-\mu^+\mu^-$. Relying on generator level simulations for data taking with the LHCb detector, we determine the reach of this facility to the aforementioned processes. We show that branching ratios as small as $9\times 10^{-12}$ ($3.2\times 10^{-10}$) and $2.7\times 10^{-11}$ can be tested at the $95\, \%$ CL respectively.