Searches for lepton flavour and lepton number violation in K$^+$ decays

The NA62 experiment at the CERN SPS is designed to conduct precision tests of the Standard Model by studying rare decays of charged kaons. NA62 took data in 2016-2018 and collected a large sample of charged kaon decays into final states with multiple charged particles. The sensitivity to a range of lepton flavour and lepton number violating kaon decays provided by this data set is improved over the previously reported measurements. Results from the searches of $K^+→ π^-l^+l^+$ decays with a partial NA62 data sample are presented.