Coating system and method for its manufacture and its use

A coating system and a method for its manufacture are provided. An electrically conductive base coat and a porous overcoat lying over the base coat are arranged on a ceramic substrate. At least one additional deposited layer is arranged on the base coat in such a way that the additional layer is formed in the pores of the porous overcoat adjacent to the base coat. The additional layer is deposited either by currentless or electrolytic deposition. For electrolytic deposition of the additional layer, the ceramic substrate sintered with the base coat and the overcoat is submerged in an electrolytic bath and the base coat is connected as a cathode. The currentless deposition takes place from a solution of the metal to be deposited with the addition of a reducing agent.