Not sure if it can be done with a "one button push" (I'm a bit tired right now, and not in front of that specific DAW). I suppose what you could do is route all items you'd like to monitor to one aux each (in addition to actual DAC outputs) and have the ones you do not want to hear muted. Then you could just swap "un-mutes" and that way hear what's going on. I guess it'd be something like:
Outputs 1-2 = main speakers
Outputs 3-4 = cue mix 1
Outputs 5-6 = cue mix 2
So you route from whatever source you want to add to a cue mix to a dedicated aux. And then the dedicated aux would have something like this:
Aux "Cue Mix 1":
Send to Outputs 3-4
Output to Outputs 1-2
Aux "Cue Mix 2":
Send to Outputs 5-6
Output to Outputs 1-2
In addition to that you would then need another aux for the actual mix; Aux "Full Mix". So your source tracks, say drums, instead of going to Outputs 1-2 would go to aux "Full Mix", and aux "Full Mix" would go to Outputs 1-2 instead. That way you can mute your full mix and unmute your cue mix of choice.
I'm guessing your routing could end up being a bit complex though with pre-fader sends at the right place in order to make sure everyone hears what they need ( - like I said, I'm pretty tired right now). But other than that I don't see how it would be done. It doesn't really seem like a better way to work to me.
Nuendo is great for this btw, with its built-in "Control Room" which does what you want and then some. But we weren't talking about that I guess...