First off, welcome to the forum.
Seems that several places I read that you can cantilever the floor joists out the thickness of the floor joists with no problem. So, for 2x10 floor joists, 9.25" would be okay. Now, if you plan to attach a deck to the rimjoist that is on already cantilevered out floor joists, it would depend on how you had the deck supported. Personally, I think that you would need a support beam under the deck pretty near the rimjoist, with the other support beam being on the opposite side of the deck. In other words, the rimjoist does not support the deck.
I'll be interested to see what others say.
Keep us informed on what you decide to do...then take pics once you build it.