  The NA48/2 experiment at CERN collected a large sample of charged kaon decays
into final states with multiple charged particles in 2003--2004. A new upper
limit on the rate of the lepton number violating decay $K^{\pm} \to \pi^{\mp}
\mu^{\pm} \mu^{\pm}$ obtained from this sample is reported:
$\mathcal{B}(K^{\pm} \to \pi^{\mp} \mu^{\pm} \mu^{\pm})<8.6 \times 10^{-11}$ at
90\% CL. Searches for two-body resonances in the $K^{\pm} \to \pi\mu\mu$ decays
(including heavy neutral leptons~$N_4$ and inflatons~$\chi$) in the accessible
range of masses and lifetimes are also presented. In the absence of a signal,
upper limits are set on the products of branching ratios~$\mathcal{B}(K^{\pm}
\to \mu^{\pm} N_{4})\mathcal{B}(N_{4} \to \pi^{\mp}\mu^{\pm})$ and
$\mathcal{B}(K^{\pm} \to \pi^{\pm} \chi)\mathcal{B}(\chi \to \mu^{+}\mu^{-})$
as functions of the resonance mass and lifetime. These limits are in the
$10^{-10}-10^{-9}$ range for resonance lifetimes below 100~ps.
