The NA62 experiment at CERN collected a large sample of charged kaon decays into final states with multiple charged particles in 2016-2018. This sample provides sensitivities to rare decays with branching ratios as low as 10 −11 . Searches for the lepton number violating K + → π − µ + e+ decay and the lepton flavour violating K + → π + µ − e + and π 0 → µ − e + decays are reported. No evidence for these decays is found and upper limits of the branching ratios are obtained at 90% confidence level. These results improve by one order of magnitude over previous results for these decay modes.