  We investigate the scalar potential of a general $S_3$-symmetric
three-Higgs-doublet model. The outcome of our analysis does not depend on the
fermionic sector of the model. We identify a decoupling limit for the scalar
spectrum of this scenario. In view of the recent LHC Higgs data, we show our
numerical results only in the decoupling limit. Unitarity and stability of the
scalar potential demand that many new scalars must be lurking below 1 TeV. We
provide numerical predictions for $h\to \gamma \gamma$ and $h\to Z \gamma$
signal strengths which can be used to falsify the theory.
