What radio stations etc do when they have a call-in show is, "open the lines" be that 1, 4, 10, etc. A call screener picks up the call gets the person's name and question and adds it to the "green room" were the host can see the callers on hold. While on hold, all the callers hear the audio from the radio station.
I got RingCentral specifically to do a call in live show "Living with Disabilities" Here are 2 companies that offer this service. Call in Studio and Blog Talk Radio. Blog Talk Radio has the nice interface, while blog talk radio has the look and feel and control a physical console would have.
Telos VOX is just one of the systems radio stations use.
Being able to control liens being open, drop caller, mute, hold, drop all callers, etc. would bring in a lot of radio/TV stations and podcasts.