Don't worry about bigger. Bigger is not better.
Yes you COULD put a 2jz-gte engine from a supra in there. It'll require extending the front end of your car and doing a massive RWD conversion, not to mention the engine and tranny.
If you do this yourself by some miracle... it'll cost somewhere in the rance of $12-15K. At a shop you're talking a $25k swap.
Search for a 3s-gte engine from a MR-2 turbo or Celica GT-4.
Let me know what you come back with.
Aside from the engine and new tranny all you'll need is new motor mounts.
2.0L turbocharged inline 4 cylinder. Spits out 200-260hp stock depending on which generation engine you get.
http://www.youtube.com/watch?v=fdptP...eature=related
Enjoy.....
http://www.youtube.com/watch?v=RfPWz...eature=related
Then go race some Evo's
ADD: Here's an in car vs a motorcycle lol. Its not a superbike but I'd like to see your stock corolla do this:
http://www.youtube.com/watch?v=srUcS...eature=related