Unfortunately, there are no other engines that will match exactly with the existing mounting points. But that could be said for other generations of the Corolla as well. Assuming you have the 1.8L engine?
The 2ZR-FE engine was optimized for fuel economy first. Typical bolt ons (header, intake, exhaust, piggyback/standalone EMS) all help the throttle response and sound of the engine, but unfortunately don't gain much (handful of HP max).
On possible option is to swap in the larger Toyota corporate motors - the 2.4L 2AR-FE (157-166HP) or the 2.5L 2AZ-FE (169-180HP). Being larger in displacement - they generally respond better to the same mods as applied to the 1.8L 2ZR-FE.
Cost, fabrication requirements, and time will be significant with an engine swap.
If you are looking at a near 200HP sleeper car with only occasional track use. Nitrous injection might fit the bill the best. Best bang for the buck, engine is stout enough for a 50HP shot all day long, some have claimed to even run a 75HP shot without issues on the stock engine.
You haven't mentioned suspension - corollas have all been tuned to run a bit soft, suspension wise, even modest upgrades to the suspension and brakes can yield huge gains in overall vehicle handling. As long as you don't go extreme with a massive drop - most people couldn't even tell you're running better springs.
Keep in mind, with any mods, larger and/or more powerful engines require additional considerations - cooling has to be accounted for, steady oil supply is critical, will the transaxle hold under power, braking system can handle the upgraded power, tires, wheels, chassis balance, etc. Its great to want more power - but it might be easier to go the opposite way. Lighten the car, sharpen the handling, traction and braking, run a larger oil sump with proper baffling - make the most of the available car instead of beating it with more power. Also, depending on the track - certain mods means you're bumped into different racing class (SCCA or NASA sancitioned events usually).