The existence of exceptional bulk, quasi–bulk–surface and pseudo–surface waves in a crystal of arbitrary anisotropy coated with a solid layer of arbitrary anisotropy is considered. One–component exceptional bulk waves that exist on the mechanically free surface are shown to disappear on the plated surface. They give rise to quasi–bulk–surface and pseudo–surface waves. The connection between the appearance of quasi–bulk subsonic surface waves and the existence of subsonic ordinary (Rayleigh) surface waves is investigated. In the plated crystal, instead of one–component exceptional waves, there arise three–component exceptional waves which involve the limiting bulk wave and two inhomogeneous modes. It is shown that the presence of an overlay in a general manner provides the existence of high–velocity (supersonic) pure surface waves near the intermediate transonic state and the existence of leaky waves near the highest transonic state.