Does a resonance structure have more than one Lewis formula?
Each resonance structure only corresponds to one chemical formula... but a single resonance structure has a fixed structure by definition of it being a snapshot of a molecular electronic configuration.
The one chemical formula can have more than one resonance structure, and typically, a stable molecule will have more than one resonance structure.
Take nitrate anion for example...
Each resonance structure corresponds to only one chemical structure, and that's the one you see on the page. In this case we just have three degenerate structures; if you rotate the first one
But that is no coincidence. This rotational symmetry is what then sensibly gives the resonance hybrid structure, which has 3-fold rotational symmetry axis through the page: