To my understanding, you can but no team bar LA will be able to afford the tax on them.
If a team is over the tax, they can only offer the MLE which is around 5 million per. Paul would obviously not sign for that. You can only go over the cap limit to re-sign players who you have bird rights to, and that's where luxury tax comes into play (although teams can enter luxury tax by using the MLE too).
Just to clarify because some people appear to be confused. Stern could only block this trade because the NBA owns the Hornets. It shouldn't be the case because it's clearly a conflict of interests but that's what allowed him to block it. He could not stop Paul being traded to the Knicks which has been suggested. Although that won't happen anyway because they have nothing to offer.
Also, Hornets were not receiving Odom and Gasol as someone stated. They were getting Odom, Scola, Martin, Dragic and Houston's first round pick. That's not a bad haul at all. I do hate the fact that the stars are turning into little wusses, demaning to be traded to certain teams. It's bullshit and is ruining the NBA, but that said, this deal probably shouldn't have been nixed.
I don't have sympathy for Lakers fans. It would have been a joke if they'd been able to land both Paul and Howard. The Paul deal I can accept, because I actually think it makes them weaker, but a deal for Howard with Bynum as the main piece would almost be as laughable as the deal that got them Gasol from the Grizzlies. Bynum is a good player, but his trade value is extremely overrated. He's very injury prone. Other teams can offer much better deals for Howard.
BTW, apparently all three teams are going to try to fight this decision and get the trade passed. Otherwise there will be a lot of unhappy bunnies at their respective teams.