I have had the CQ20 for barely a week to prep for a future band proj early next year. Mute groups would be benificial for variations. It can be done using scenes, each scene having required mutes bu you have to remember to save the scene mix each time or any scene recall will put the faderss back to a saved status, problem if you have adjusted a mix on the fly. Example as previiusly commented, mute all inputs except the background music/interval. Doing this via a scene of muted channels works but you have to make sure the live scene has saved fader levels and indeed any other adjustments on the fly.
I still have to investigate all the available functions for possible work araounds.
fX muting for talkover, there is a function buried in the footswitch settings that in fact mutes all FX if anybody is interested.