Luminos has the right of it, not stunts just rules for additional ways to spend fate points. Perhaps the costs need to be bumped a bit, but I think you should be able to pull of more than just bonuses on rolls, rerolls, or even invokes for effect (as wide as that option is) with them.
Maybe, for instance, a creature with Inhuman recovery could buy an upgrade to it for a scene with an adequate fate point expenditure for example.