The NA48/2 experiment at CERN collected a large sample of charged kaon decays to final states with multiple charged particles in 2003–2004. A new upper limit on the rate of the lepton number violating decay is reported: at 90% CL. Searches for two-body resonances X in decays (such as heavy neutral leptons and inflatons χ) are also presented. In the absence of signals, upper limits are set on the products of branching fractions and for ranges of assumed resonance masses and lifetimes. The limits are in the range for resonance lifetimes below 100 ps.