I don’t think that’s possible. Representing more exact ints means representing larger ints and vice versa. I’m ignoring signed vs. unsigned here as in theory both the double and int/long can be signed or unsigned.
Edit: ok, I take this back. I guess you can represent larger values as long as you are ok that they will be estimates. Ie, double of N (for some very large N) will equal double of N + 1.