Don't take my post to imply that I personally hold that there IS anything which is supernatural. But just as I can contemplate what WOULD be the attributes of Santa Clause, I can do so with the supernatural.
And I felt that the separate 'two states' view in the OP was not necessarily how it had to be looked at. So, the questions based on that may not be that interesting to pursue.
I don't directly define the natural universe to encompass all things of existence. Rather, I have found no reason to think that anything exists which is beyond (or above/behind/around) the natural universe. But, in principle at least, the 'possibility' for them exists under the definition I use for the natural.
And while we may find numerous 'new' natural laws, I don't think that too many theists would consider God to be bound by such, therefore always allowing him to be beyond the limits of the natural.