Short answer: use a virtual cable
I needed a mix that included my DAWs metronome and the OS sounds ( Chrome, VLC, etc) along with the DAW mix. But I didn’t want the streamed mix to contain the metronome. Mix 1 is the only one with the OS sounds but if you download a virtual audio cable and set windows to use that as the playback device, you can then add a track in your DAW with that as input and you then send that to mix 2, 3 or 4.