We present preliminary COMPASS results on kaon multiplicities produced in semi-inclusive deep inelastic scattering of 160 GeV muons off a pure proton (LH$_2$) target. The results constitute a large data set of more than 600 points for pions and 600 for kaons, covering a large $x$, $Q^2$ and $z$ domain in a fine binning. The results from the sum of the $z$-integrated multiplicities $\mathscr{M}^{K^+}+\mathscr{M}^{K^-}$ and their ratio $\mathscr{M}^{K^{+}}/\mathscr{M}^{K^{-}}$ are presented versus $x$ and compared to previous COMPASS results on deuteron and other experiments like HERMES.