I think you want to achieve what I am also doing ..

Sending different types of audio (coming from different sources) to different channels (TM FX middle row "Software Playback Channels") and finally to create the perfect submix for your monitors and phones individually.

Is it that ?! This is easily possible with TotalMix FX.

Some month ago I got such a concrete demand / use case.
I was listening to a long youtube video about a computer game, but I wanted
- to listen to it in the background
- play the game
- listen to some nice bachground music.

Isi pisi ... I changed all of my TM FX routings to support the following
- SW Playback 1/2: everything from the OS / Youtube / "Windows Sound" (through WDM driver AN1/2)
- SW Playback 3/4: music from MusicBee player, supports ASIO, so send music to AN3/4
- SW Playback 5/6: audio from games (if your game supports selection of other audio output), through WDM driver AN5/6

The setup of Windows, MusicBee and Game to send audio to these channels was easy (AN 1/2, 3/4, 5/6).

Then in TM FX submix mode select a particular HW output (TM FX bottom row) e.g. phones channel
and create the submix by
raising the  faders of SW Playback 1/2, 3/4, 5/6 in a way, that you get the perfect submix:
- Youtube video a little bit louder                (fader of SW Playback 1/2 at 0dB)
- MusicBee background Music not so loud   (fader of SW Playback 3/4 to -10 dB
- Game in between both                             (fader of SW Playback 5/6 to -5 dB in my case)

Need a submix for your main monitors as well ? Select HW output channel for your monitors and now change fader positions as above as you need for the normal business (potentially all at 0dB as default setting).

The final routing you can store to snapshots as you want.