  A search for the $K^+\to\mu^-\nu e^+e^+$ decay, forbidden within the Standard
Model by either lepton number or lepton flavour conservation depending on the
flavour of the emitted neutrino, has been performed using the dataset collected
by the NA62 experiment at CERN in 2016--2018. An upper limit of $8.1\times
10^{-11}$ is obtained for the decay branching fraction at 90% CL, improving by
a factor of 250 over the previous search.
