If you have a high-precision test and a precise source of a particular chemical it can be done. The hard part for me has been knowing the precise amount of chemical you have.
If it were me I would use something like CalHypo. I would first determine precisely how "strong" my CalHypo was by adding a precise amount to a precise amount of water. For example, adding 20 milligrams of CalHypo to 5 liters of distilled water (tap water already has chlorine). Then I would test that by filling the chlorine test kit to 25 mL so that each drop is equal to 0.1 ppm. If I measured 2.6 ppm I would know my CalHypo registers 65% chlorine on the test.
2.6 mg chlorine/L x 5 L = 13 mg chlorine
13 mg chlorine / 20 mg CalHypo = 65% chlorine
Then I would weigh out to a precise number of grams to add to the pool (maybe 200g or so). I would dissolve it in a pitcher first and then add it the moment the sun is no longer on the pool and let it mix for a couple of hours with the filter running. I would use the chlorine test filled to 25 mL again to measure the chlorine levels before and after the addition.
For example, you test your pool's chlorine to be 4.7 ppm. You add exactly 200 grams of CalHypo and after mixing you measure 5.9 ppm chlorine.
So we now know that 130 grams of chlorine (200 g x 65%) raises your pool by 1.2 mg/L (ppm).
The rest is math (and in school you asked why you needed this math):
130 g / 0.0012 g/L = 108,333 L / 3.7854 L/gallon = 28,619 gallons
You have a big pool
Don't forget each step has a margin of error, and they stack up as you move through the process. For example, if your scale is ± 0.001g your CalHypo could be anywhere from 62% to 68%. If the chlorine test is also ± 1 mg/L (ppm), that makes your CalHypo anywhere from 59% to 71%. Then you'll experience another ± 1 mg/L error when measuring the final chlorine level in the pool, making the possible range of actual pool size between 24,200 gallons and 34,100 gallons