Rare decays with dimuon and multimuon final states provide clean tests of the Standard Model at the LHC. This proceeding summarizes recent ATLAS and CMS results on $B_{(s)}^0\to\mu^+\mu^-$, including branching-fraction measurements and effective-lifetime information, together with the first Run~3 search for $D^0\to\mu^+\mu^-$ and the full Run~2 angular analysis of $B^0\to K^{*0}\mu^+\mu^-$. The overview also includes the observations of $J/\psi\to4\mu$, $\eta\to4\mu$, and $\Lambda_b^0\to J/\psi\,\Xi^-K^+$. These results define the current experimental picture for rare-flavour studies at ATLAS and CMS.