Rather than move up in weight he needs to work on his defense. Truth be told there are not many fighters who would stay up from the shots that have put him away, some would argue that this is what separates the greats from the good/average and I wouldn't exactly disagree.
Larry Holmes could have lost to Shavers, Fraizer could have knocked Ali out, Mosley could have lost in the 2nd ( or 3rd?) round to Forrest), Mayweather could have an embarrassing loss to Mosley, Bradley record could show a loss to Holt. List goes on and on.
I guess having a good chin is important when you want to compete at a certain level as in 36 minutes of boxing you're likely to get caught with something vicious. The fact that Khan crumbles when that happens is something he will have to live with and something he will have to try and negate by being extra cautious.
That's why I disagree with people saying he should team up with Pernell Whitaker or Roger Mayweather, they could help him on his defense however the defense they operate is very precise and ****ing up once could lead to him getting tagged. Which is why I think he should team up with E Steward, someone who can help him use his jab to stay far away from his opponent. He also needs to work on doing that for a full 12 rounds so that he can do that for the full 12 rounds, failing that needs to work on his defense on the inside so that if his legs go punches won't find their way through the guard.