I have to ask, though…what does running two comps do that can’t be done with one?
A number of possibilities.
First: serial compression is incredibly common in the studio because multiple comps running at lower ratios sound more natural than a single comp run at a higher ratio (even if the effective ratios are equivalent), and that's why some gigging musicians do it.
As noted by others you can get scientific with this, e.g. using the second comp at higher threshold and higher ratio. But one introductory article I read said "just clone as many low ratio plugins as you need until you get the result you want".
Next, some use one compressor for gentle smoothing, and another at the end of the chain as pure limiter, to catch stray peaks (such as plugging in your bass at full volume).
There are also specialty uses: a general comp, then another to go along with a certain effect such as filter or octaver.
Yet another: many like to have a transparent comp at the beginning of the chain for general smoothing, and then a flavorful comp at the end of the chain for tone (tube compressors are popular at the end).
Side note: for rock I always use overdrive/distortion which adds inherent compression, but especially if I'm using tube-style overdrive I also like to add a compressor to simulate the response of a pushed speaker cabinet. With my old SVT rig, the magic happened when cranking it up: pushing the power tubes into clipping, but also pushing the limit of the 8x10 enclosure. (I never got to do that often enough, but I'd hate to think of what my hearing would be if I did...)