You have the math concept right.
Many compressors bring the higher volumes down. However, the last adjustment inside a compressor (usually labeled Output) can be used to adjust the overall output that comes out of it back up .. so everything that went through it can be adjusted to be louder without clipping. Meaning first you lower the peaks, then you can bring everything back up, resulting in louder overall sound.

Most Compressors do this.
Good ones do it well.

Mastering FX Suites (which also include peak limit/loudness maximizers and other tricks of the trade) are really what you need to make it work. Try the free trial of Ozone in the Output Insert of #1. But don't get mad at me when you realize you need to buy it. I'm just the messenger.

It IS possible to use PGPeakLimit to vastly improve the volume of the Output in the final wave, but (being free) it it is not comparable.

If looking for other possible free options, T-Sledge may work .. but again not really comparable to something like Ozone.


I do not work here, but the benefits are still awesome
Make your sound your own!