There is a very good basic formula for rate of climb. Not infallible, but pretty good for an estimate.
RC = 33000 * (PA - PR) / W, where PA = power available (hp). PR = power required for level flight, W = Weight (pounds). RC = rate of climb (feet per minute).
Take a Hawker Sea Fury. Normal specs for a Sea Fury FB.11 show: Gross Weight = 12,350 lbs. HP at sea level = 2,480. Known initial rate of climb = 4,320 fpm.
Solving using the formula allows us to solve for power required: PR = 863.2727 hp.
So, if we let the weight drop down to, say, 10,400 pounds, we can estimate a rate of climb at 5,130 fpm. At that weight, there isn't much fuel or ammunition left, so the sparkling performance won't last for long or do much good, other than to support the lifestyle and feeling of power of the pilot.
The Vought F4U-4 Corsair has almost the same specs. Gross weight as a fighter = 12,405 pounds. HP at sea level = 2,400. Known initial climb rate = 4,360 fpm.
Solving for power required gives = 761.0364 hp.
Again, if we let the weight drop to, say, 10,400 pounds, we expect a rate of climb of about 5,200 fpm. These two planes perform almost exactly the same, with very similar expected climb at very light weights.
Both planes only have these climb rates at war emergency power (2,400 hp or so), with the throttle breaking through the wire stop. At normal military power (1,500 hp or so), both are considerably less sprightly in climb. For both, I'd expect a cruise-climb at 2,000 - 2,200 fpm for most operations. Max rate of climb would be in the heat of combat, not normal flying.