The only possibility to achieve that is to send your monitoring signal to a 2nd output of Apogee.
There, you connect the output with an input of the Multiface (preferable a digital input).
DIGICheck can be a clock slave to the Apogee.
In DIGICheck select the Multiface driver to monitor the digital input of your Multiface.
In the DAW, use the Apogee driver.

I don't know how far your considerations have progressed, and your decision has been made, but I would like to offer you an alternative. Current RME devices also have top converters.

What you could try as an alternative:

Option A) if you only want to improve your monitoring: Keep Multiface II and connect one of the reference converters (ADI-2 Pro FS R BE or ADI-2/4 Pro SE) via ADAT or SPDIF (preferably optical). The A/D and D/A conversion is always done via the internal FS clock due to the device design, regardless of whether the ADI-2 * clock is master or slave.

Option B) UFX II or UFX III alone. Both devices have the AKM converters from the ADI-2 Pro FS reference converter. New features such as Room EQ and Crossfeed have been added. If it should be a smaller interface: UCX II.

Option C) UFX II / III (or also UCX II if you prefer a smaller device) in combination with the reference converters (similar to A) to get the device-specific advantages here too. The reference converters can be easily controlled via the ADI-2 Remote software.

All in all, you would retain DIGICheck and all interfaces would have excellent D/A conversion quality.

Here how to integrate such a reference converter, connected via AES or ADAT/SPDIF to your environment:
https://www.tonstudio-forum.de/blog/Ent … our-Setup/

About the quality of RME products in terms of converter quality, please watch this video. See and listen (the original wav files can be downloaded) which devices RME is competing against here and also offers much more (in terms of features) compared to the pure A/D converters in the €5000+ price range.

Mastering Converter Shootout with the ADI-2 Pro FS
https://www.youtube.com/watch?v=doHG32aXBDY
WAV files: https://www.youtube.com/redirect?event= … oHG32aXBDY

Regarding some cool features of the reference converters:
https://www.tonstudio-forum.de/blog/Ent … ses-EN-DE/