Deadman, remember that our BATF sometimes tries to make busts for "conspiracy" to violate the National Firearms Act of 1934, so we're extremely cautious. And you've left your location blank.
It's completely *possible*. And under US law, legal so long as you also stretched the barrel. I think the stock would have to be permanently attached though, or only removable in a fashion that left the gun unable to function as a handgun (of the stock was set up as a "quick detach" versus bolt-on).
The easiest plan I can see would be to take the factory grip off, then bolt a plain rod of metal the width of the grip frame to the bottom of the gripframe, running backwards and then supporting a shoulder stock by coming upwards at the end. Then just carve a bit out of the rubber grips so they'll fit back on with the extra metal in place.