Beyond seconding what's been said about the inadvisability of applying a veneer to the plastic, I'd point out that you may well have thick plywood under the plastic sole. That gives the floor strength and rigidity.
In that case, all you'd need would be thin, i.e. 1/4 or 3/8 inch veneered plyood over the plastic. In such a situation, the only purpose that top layer of ply serves is as a base for the veneer.
And you do need a wood base for the veneer. Even then, gluing alternating strips of paper-thin teak and holly parquet to a proper wood surface is quite an art.