If time and money were no object - then there is nothing stopping you from swapping in "any" engine. Why stop at those turbocharged 4-cylinders - you can stuff in a V8 (has already been done), install a rotary engine, convert from FWD to AWD or RWD, etc.
The basic/gross conditions for any engine swap - first is legality, second is physical dimensions and locations of the driveline, third are electronics. If the swap cannot be registered for the road - there is no sense even starting it. No fun to swap in a killer driveline if you are not allowed to drive the car on the road - if this is a pure track car (trailered to and from the event), then this is a mute point. If the engine is too large to "fit" in the car, you'll have to do extensive modifications to the chassis, run a huge risk of upsetting the chassis. Again, bad news for you, if you drop in a powerhouse, only to have to shear the front subframe off once you drop the hammer. Depending on the driveline/engine choice - would be easier to drop the Corolla "body" ontop of the donor vehicle. Electronics and tuning are the key to making any engine swap driveable. The amount of wiring can be staggering, you might have varying amount of support - depending on the engine and what features you want to keep. Good example are ABS functionality and interior gauges. Depending on the swap - the donor engine's ECM may not like anything other than the special "box" inside the original gauge cluster (ex. the Mazdaspeed3).
Interesting you pointed out those particular cars. Granted, they are powerful FWD platforms, but they will unlike take a Mustang or Camaro, unless they are V6 powered variants or the driver is asleep. The amount of money and time to get those to "work" in the 7th generation Corolla is not for the faint of heart.
An alternative solution to get the sleeper look and significant gains under the hood - you don't have to look any further than Toyota's own engine/driveline offerings. The 4AGZE 1.6L factory supercharged engine will almost drop into your 7th gen Corolla with minimal modifications. In stock form, they can crank out up to 185HP with the S/C. Popular engine choice to turbocharge, as the engine is already designed for boost. With the appropriate tuning and setup - 250-300HP is attainable. Toyota's legendary 3SGTE 2.0L factory turbocharged engine is known to be a huge power builder with minimal modifications. In stock form (US models) put out 200HP. That is seriously "detuned" by the manufacturer, this engine is typically handicapped at 50%-75% of its available power. 300-350HP is typical for this engine with stock internals. Again, this is a well known swap into 7th gen Corollas, there are also quite a few out there. Both made they name in the Toyota MR2 - the 4AGZE was also available in the Corolla platform, making it a good choice for boost applications.
Looking for something different - megapower levels! Toyota's 2JZGTE 3.0 inline-6 turbocharged engine from the legendary Toyota Supra, (US models) peg it at 320HP. Bolt ons and tuning yield 400-500HP on the stock bottom end. Beef it up and power levels are staggering for a small displacement engine. Granted it is a RWD platform, but if money is no object, why not convert the 7th gen FWD Corolla into a RWD platform. Better weight distribution, better weight transfer to get the power to the ground, and a novel solution to eliminate the understeering nature of almost all FWD platforms.
Don't forget the N/A platforms as well. 4AGE (16v and 20v variants), 2ZZ-GE, 3SGE "Beams", etc. Lots of choices in the Toyota family.