You can go in and manually annotate a given component instance, to have an arbitrary physical designator (at least since AD14), but I'm not sure about "part" (i.e., suffix).
For sure, it would absolutely screw with the other underlying purpose of sheet instances: repeated placement/routing. Channels would have to have mismatched components and routes, which is dumb.
At least with the ready availability of compact singles and pairs and such of common parts (logic gates, op-amps..), it's not a big deal.
(As an aside, amazingly enough, it's *possible* to do this in Multisim/Ultiboard, at least as of the version I last used. But, Multisim absolutely will not respect manual designator assignments, and will randomly reset all your careful work. And can't be back-annotated into submission, because it thinks all the parts are new and separate. So, yeah.)
Tim