The biggest _I'VE_ ever put on bone stock OEM wheels are 315x35x17 -- they fit fine. No bulging, and i believe that if your struts arent blown, you wont have any rubbing problems either. I would rub SLIGHTLY on big bumps at high speeds.. however, my struts were totally blown.
Nitto's in 315 would fit perfectly fine, and Yokohama AO32R's would fit perfectly fine. Even tho both tires are "315" -- they are NOT the same width. The AO32R is actually wider then the Nitto, and there are certain brands that are usually wider then other brands.. ie. RE71 Potenzas were wider then other brands in the same size.
Here are some pics... from multiple angles:
Stock wheels, from straight behind, with Yokohama AO32R's (Road race tires)
I would suggest against running 315"s on stock Supra rear rims. All issues having to do with the fenders and springs aside - the minimum recommended rim width for mounting a 315mm tire is 11". I have 10.5" rims and I would only go 295mm on them. I should add that I am running 275/35's on 18" x 10.5"s, and the handling is just superb. I personally do not recommend running 275's on the stock rims, if you care about handling (more about this below). If all you want to do is dragrace - slap on some 275's and be done with it. Another option is to use a set of rims just for driving on the street, and have some rears ready for the dragstrip...
The Viper runs (17" or 18") x 13" rims - and has 335's out back... I don't feel like doing a ratio analysis on 17" x 9.5" : 315 compared to 17" x 13" : 335, but if you did, I'm sure it would come out to a crazy difference. Yeah.
I had the unfortunate displeasure of running 275's (Yokohama A520's - suck) on my stock rears... it was my 2nd set of tires. I feel it was the worst 7000 miles of the car's life, and I was just WAITING to get them off - the problem being that the rear end felt very "loose" because of the higher sidewall. I wonder why I didn't just take them off earlier. (The stock Bridgestone RE022 tires lasted me 9000 miles.) After the A520's finally wore out (I took advantage of every possible opportunity to squeal the tires
and chirp through the gears - but with a treadwear of 300, yeah). I was so happy to finally get them off.
so... my advice is to not sacrifice handling in the name of looks... If you do feel that you have to do that, get a separate set of rims for that purpose, and don't try taking turns too hard when you have em on... this is just from my experience.
What Rasidel says may be true. I dont autocross my car, i dont take corners fast, i dont really care too much about handling.
My car goes in a straight line, and gets me to and from work.
I enjoyed every minute of driving my car with those wheels and tires... I never felt that the cars performance was significantly hurt in that department, and when i bought the car, it had much smaller wheels in back.
I have 315's on 11" wheels now, and the same exact tires up front, and still have no problems. Granted, the front WHEELS are wider now, but not the tires.
Regardless, the question was asked "what is the biggest" -- and 315's are about the biggest you can get.
Some people like it, some people dont. I personally, loved it.