If you're up against an opponent who 3-bets too frequently preflop, it stands to reason that you could profitably 4-bet shove against him because a large portion of his range would be forced to fold.
I don't know exactly how high an opponent's 3-bet percentage needs to be to make a 4-bet shove profitable, but math and PokerStove indicate to me that it's somewhere between 15 percent and 20 percent, according to a couple of scenarios I wrote out. I think it's fairly safe to say that you can 4-bet shove profitably against someone who's 3-betting more than 20 percent of their hands preflop over the long run. CTS also mentions the possibility of 4-bet shoving in his famous 3-bet post.
For a week or two, I tried 4-bet shoving against opponents who reraised too often. I put my 4-bet shoving range around 88+ and AQ+. My relatively small sample showed negative results.
There are a few problems with 4-bet shoving in shorthanded NL cash games:
_ If you 4-bet shove all the time instead of making smaller 4-bets, you can't ever 4-bet bluff. 4-bet shoving limits your range and your options. jcl touches on this point in his excellent CardRunners series, "Making the Jump."
_ It only really works when you're out of position. A 4-bet in position narrows your range too much, especially if you ever want to be able to call a 3-bet. However, out of position 4-bets may be more reasonable than in position 4-bets because you should pretty much never be calling a 3-bet out of position. It's a raise or fold situation.
4-bet shoving has its place, especially in some players' heads-up strategies. But it's applications are limited in shorthanded and full ring games, and it detracts from a well-rounded overall strategy.