Yes, I've seen some under-mount Class 3 hitches at etrailer.com that actually have a 1¼" shaft that pushes into the class 2 hitch, using that as a support. This would be a very rigid mount by using the class 2 hitch, plus 4-6 bolts underneath. You then have a plate in front of the Class 2 hitch/shaft so it doesn't look so stupid.
But if that isn't what you want, you go to a junkyard or dealer to find the Class 3 hitch and swap it out. Seems like you have to pull the bumper cover. No big deal.
The biggest issues, like the half-dozen others threads I've replied to today, is that this will do absolutely NOTHING to increase your tow rating. Unless you also changes your axle gearing from 3.55 to 3.73, you are still drivetrain limited, and still stuck at 3500 lbs max rating.
The only benefit I have heard of from swapping is if you are remaining under the 3500 lbs limit, but you need more tongue weight rating. Like a large popup camper that weighs 3000 lbs, but has 400 lbs tongue weight. In that case, the Class 3 hitch will get you the TW rating you need, but you are still limited to 3500 lbs max trailer weight (with only a driver in the truck).