To MOVE an existing listing, use the "Update URL" in the CURRENT category.
To suggest a listing to a second category, use the "Suggest URL" in the PROPOSED category.
An editor could take either suggestion as an opportunity to review any aspect of the site's placement, so the effect MIGHT be the same in the end.
Or the editor might just see an obviously unreasonable request and delete it out of hand WITHOUT considering what else might be worth changing about the listing.
So the more specific the suggestion, the more likely the editor will CONSIDER exactly what you suggest. (That doesn't mean he'll do it, of course -- the editor is responsible to the community for following the guidelines, and for using his own best judgment.)