Remember that a 3" shell has no higher pressure ceiling than a 2 3/4" shell. Of course it will recoil more, but that's because of the heavier shot charge, not higher pressure.

And if someone extended a forcing cone beyond the forend lug, that might be some sort of world record for longest cone. I suppose backboring is a possibility, but it would seem a bit odd to do that on an inexpensive Turk gun.