Depends on the amout of miles on the car, version of engine, transmission, and your definition of a lot of money.
The 1993-1997 Corollas were available with either a 1.6L or 1.8L inline four mated to a 3/4 speed auto or 5 speed stick.
If you have the 1.6L - not much you can do with about power at those speeds. The 1.8L is a bit better (more torque) but not much more in HP.
The three most common performance mods you can do - improved air intake (ram or CAI), better exhaust (headers, cat-back), and performance ignition system (plugs, wires, coil) will help out at the higher RPMs and WOT - but you will sacrifice some low speed HP and torque (intake and exhaust upgrades).
Cost: $200 for used - $400 or more for new.
Gains: 5-7 HP and 3-7 ft.lb torque (High RPMs - WOT)
Loss: 3-5 HP and 1-5 ft.lb torque (Low RPMs)
Other possibilities - under drive crank pulleys - will give you about the same gains as a CAI and exhaust combo but without the low RPM penalty. Problems - runs the alternator slower, chance that it will not charge the battery enough. Also runs the accessories mcuh slower - may cause problems later. Cost - about $200 to $400 for a set of pulleys.
Other alternatives - Turbochargine, Supercharging, NOS, engine swaps, performance head replacement are a weekend job and much more expensive.
But before you start spending big $$$ with upgrades - look into what you have to work with. Check to make sure that the air filter is clean and the airbox does not have any obstructions, PCV valve is free and not sticking, clean intake ports and injectors (run some good fuel injector cleaner), clean the throttle body, and check or replace the fuel filter. Basically a comprehensive tune-up. Will take about a day and even with dealer priced parts - set you back about $60-$75 and you easily gain a few HP.
If you have already done a tune-up - look into the recent upgrades that you put in the car. If you run a good sized amp - it will put a heavy load on the car. As well as any weight you add to the car - curb weight is ~2500 lbs, a hundred pounds extra will hurt high speed transit. Even in my ride - a sprint from 70MPH to 80MPH doesn't happen very quickly. Running up a constant grade also has me gAssing it more. That's comparing 125HP/125ft.lb to 105HP/110ft.lb and similar curb weights (****uming both 1.8L, auto trans if 1.6L, then 100HP/95ft.lb). A Celica GT-S would be better at that speed, but your looking at 180HP/130ft.lb.
I'd just save up for the new car and do regular maintenance on the 1996 Corolla. To get the performance that you may be looking for, a 25HP to 50HP boost probably would be neccessary. That ain't going be cheap.
Good Luck.