I recently sold my 4.0L turbocharged V6 that had a TR6060 trans/driveshaft/8.8 rear end.
It was indeed a real sleeper, lol, and dyno'd 368rwhp/398rwtq on light boost/91 octane..on bone stock engine. To me, driving it vs. a new stock 2012 GT (base coyote), there was no significant difference in the power and handling (with it's upgraded suspension).
I could easily have hit/exceeded 400 rwhp if I wanted to, but this was more of a street car and I had no desire to see how much power I could make with it. It was a very very fun car to drive, for sure! The 6-speed trans made it so much fun.
Now, this car was set up this way back about 10 years ago (by the previous owner), and he had put in a Pipeline turbo kit, the trans adapter plate mentioned by Jim, and the transmission/driveshaft/rear end. I don't know how much $$$ he put into it, but it was quite a bit.
The ONLY mods I made were to put in a different engine (the previous owner ran it lean and detonated/chipped a piston), added nissan valve springs, and changed/rebuilt the rear end/gear change (the 410's were too much for street/highway use).
There are no longer any good new turbo kits available for the 4.0L; there's one or two cheapy knockoff setups out there that have been untested, and look a little iffy at best. Several people have made their own setups or modified signle kits for a 4.6L to fit, and that's an option.
And, for the power levels you're talking about, you'll need a turbo setup to do it. Belt-driven supercharger setups, while still very fun and an give you 300-340 rwph, are still available and easier options. And of course, the engine can easily handle it.
If you want your car to 'look like' a v6 from the outside, dropping in a v8 is, IMO, a better option, especially if you can get an entire donor car (a GT). I came across such a donor about a year ago, and now that whole drivetrain is in another 4.0 v6 body, that I daily drive. Sure it's not as much power as the 4.0 turbo had, but I am very happy with it for how I use it, with its bolt-on mods and custom tuning. And, I can always slap on a low-boost blower if I want to easily jump into the 400's on the stock internals. Cost-wise, the entire donor, swap, mods, etc. was less that the cost it would take to upgrade a 4.0L, since the donor had the transmission I wanted, rear end, engine, etc...everything...at a much more affordable price than any 4.0 blower setup would cost. Just my 2 cents.