The first search for the lepton number violating decay K+→π0π−μ+e+ and lepton flavour violating decays K+→π0π+μ−e+, K+→π0π+μ+e− has been performed using a dataset collected by the NA62 experiment at CERN in 2016–2018. Upper limits of 2.9×10−10, 3.1×10−10 and 5.0×10−10, respectively, are obtained at 90% CL for the branching ratios of the three decays on the assumption of uniform phase-space distributions.