Nice one Chev!!!! (He's only saying it because it's true!)
Jakeyboy... In civil ATC nothing is laid down in writing, although the system can be adjusted to prevent dangerous overloading. At busy times it can be a dozen, maybe 20 or more....
I don't know about the military - many moons ago they used to have a limit on the number a controller could have on frequency at one time but I don't know if that still applies.