CD Players With Balanced Variable Outputs?

Rather than browsing through a long list of higher end models, I'll show my ignorance here. Is this combination available, or are these two features together incompatable?
Cary 303/300 does...not sure if other Cary's do. Output level is adjusted from remote in 63 levels
Levinson 39/390S
Almost any Wadia.
Classe CDP-102 / CDP-202

Ktennis, what exactly do you mean by
"Balanced Variable Outputs"
McIntosh MCD 201
My question about "balanced variable output" means,I think, both together. It seems many CD players have have either balanced XLR outputs plus RCA unbalanced outputs, or fixed and variable RCA outputs, but not balanced XLR outputs with a variable volume capability. Sorry for any confusion. I suppose some of the units mentioned above have this variable XLR output I'm asking about.
Resolution Audio Opus 21
Theta Miles (balanced-optional)
Monarchy Audio Model 33 DAC (requires a transport)

I've owned all of the above......

- Opera Audio "Droplet"
- Audio Aero "Capitol" series
Shanling T-100 cd player or T-200 SACD players. Both tubed or solid state outputs on the same machine, plus a tubed headphone amp built in as a free bonus....

Good sound, good looks, fully appointed, it's a winner.
Cary 303/200 and Cary 303/300
Cairn Fog

I'm guessing that he needs balanced outputs that have a variable volume control.

APL Denon 3910
"I'm guessing that he needs balanced outputs that have a variable volume control."

Alas, that was the intent of my question. My limited understanding is that many players, perhaps not the very best, "lose something" when using the variable outputs rather than the fixed outputs. Does this change if the variable outputs are run through XLR balanced outputs.
Springbok - is the variable output an option on the APL/Denon 3910? (My understanding was that this unit had fixed outputs only).