We study generic effects of new physics on the rare decay modes $$K_L \rightarrow \pi ^0 \nu {\bar{\nu }}$$ $K_L\to {\pi }^0\nu \overline{\nu }$ and $$K^+ \rightarrow \pi ^+ \nu {\bar{\nu }}$$ $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ . We discuss several cases: left-handed neutrino couplings; right handed neutrino couplings; neutrino lepton flavour violating (LFV) interactions; and $$\Delta I =3/2$$ $\Delta I=3/2$ interactions. The first of these cases has been studied before as it covers many new physics extensions of the standard model; the second one requires the existence of a new light (sterile) right-handed neutrino and its contribution to both branching ratios is always additive to the SM. The case of neutrino LFV couplings introduces a CP conserving contribution to $$K_L \rightarrow \pi ^0 \nu {\bar{\nu }}$$ $K_L\to {\pi }^0\nu \overline{\nu }$ which affects the rates in a similar manner as a right handed neutrino as neither one of these interferes with the standard model amplitudes. Finally, we consider new physics with $$\Delta I =3/2$$ $\Delta I=3/2$ interactions to go beyond the Grossman-Nir bound. We find that the rare kaon rates are only sensitive to new physics scales up to a few GeV for this scenario.