I know that a 120/90 will fit just fine, as well as the 2.5" rim to go with it, as I have these on my 550 with plenty of room to spare.
A 130/80 on a 3" rim would be no problem at all. After that the brake stay is going too be the first thing that gets in the way, but this could be modified for additional clearance without much difficulty.
I believe that a 140 or 150 series tire could be done with a little modification to the brake stay, without any swingarm problems at all. After that though you're going to be getting awfully close to the chain and the swingarm.