Microphones don't but the systems certainly can. I've done a number of large (24 to 100+ input) audio systems with only a master volume control, between AGCs and automixing you can make a 'hands off' system for many applications where the system does handle the adjustments automatically. Most of these systems were boardroom and conferencing applications and you wouldn't typically want to use this approach for theatrical applications, but it may turn out to be what was installed in this particular case.There should be should be somewhere, probably in your booth where there's some audio stuff. Microphones don't just auto adjust.
Just a suggestion, but before you go making modifications or adding anything to the existing system, you might want to invest some time in determining and documenting what you do have including what equipment is in place and how it is wired. I have a feeling there is some other equipment involved that you haven't noted, like maybe some amplifiers and stuff like that. Knowing what you have and how it is all connected can assist greatly in operating the system effectively now as well as in planning for any potential changes or improvements.