In the pursuit of physics beyond the Standard Model, a promising path is the study of B-meson decays caused by the transition $b \to s\ell^+\ell^-$. A key observable in such decays is the ratio $R_K$, which measures electron--muon universality in $B \to K \mu^+\mu^-/e^+e^-$. At first sight, the recent LHCb measurement of $R_K \sim 1$ may seem to largely constrain deviations from universality in these decays. However, we show that this is actually not the case: new sources of CP violation allow for significant universality violation consistent with $R_K \sim 1$. This provides an exciting new opportunity to search for New Physics by measuring differences between CP asymmetries in $B \to K\mu^+\mu^-$ and $B \to K e^+e^-$.