Yeah, to futher qualify what he said, if you get 17 rims, you could get a lower profile tire, keeping the diameter the same... you really can't get much wider with stock rims, and keep the same diameter.
You will need some after market rims, and if you are going to spend the $$$ on rims, why not move up to 17's in the process? Get some rims (tirerack.com) 17x7.5. You can go 235 / 45 or 50 and you will be good.. or in the ball park.
Go to a local tire dealer, and they will tell you the same thing..
Wider is about at its limit for your rims. The diameter of the rim is bubkis, you need to be concerned with the diameter of the WHOLE tire not just the rim.. the height is the rim diameter PLUS tire height, keep that in mind.
If you increase diameter of rim, you will have to lower the profile of the tire to compensate to keep the WHOLE tire the same size.. which keeps your speedo the same, and odometer.. etc..
You want the same revolutions per wheel as you do now.. probably 700 rpms per mile. to do that, you need to find an equitable rim with lower profs tires, to give you that ~700.