It's an often used technique, actually.
Many engineers have 'ganged' compressors for various reasons and effects.
Even if you're not going for the parallel compression technique, sometimes serially ganging compressors actually can do a better job of managing peaks AND RMS when they are set to process minimally rather than drastically.
It's like moving air slowly rather than causing an explosion, so to speak. If you only want to bring up the lower amplitudes without overly affecting the peaks, this is one way to go about it.
So yeah, it's a viable and often used approach.
And btw, you can have as many compressors as you want on a bus or track.