Look here what is said about the Allo.
The Ifi will be rather smooth with the Burr Brown, neutrally tuned with a touch of warmth.
Here’s the link to the one I’m talking about:
Might be a bit too much for Stax because of their immense resolution and neutrality.
I would really go in the direction of warmer with natural resolution.
But of course that’s a matter of taste.
Regardless of the budget, I would suggest foilgendes for now.
See what they lack in the Stax and what would be desirable and then narrow it down according to budget.
If the Stax amplifier is tube-driven, you would also have the possibility to play with tubes in order to round off the whole thing.
The RME Adi Fs 2 is also supposed to be a good step up for Stax.
It is quite popular on the German side, and German Stax listeners also rave about it.
It wasn’t my personal taste, it sounded too neutered in the music for me.