All around headphone amp recommendations

Not enough info to go on here to make a meaningful recommendation, and I’ve got better things to do with my time than take shots in the dark. I’ll just say you’re better off driving the headphone amp from your Classe pre if you can because it’s probably a much better preamp.  Good luck.

I second the Moon 430HAD. 
 

If you are looking for something portable Chord Mojo2 is impressive for the money. 

My main headphone amp is a Moon 430HA, but it seemed a little out of line with the rest of the system components, but it is (almost) full-sized.  Again, budget would be super helpful when asking for recommendations.

A headphone system can be simply breathtaking. Happily I finally found that out. Unfortunately, your requirements for size and price preclude me recommending the stuff I have. But, you might want to have a look at my system and consider this kind of thing for the future. I am in complete awe each day when I turn it on and listen. It is now located on the bottom shelf of my coffee table in front of the fireplace and gets used every morning, so it isn’t the centerpiece of the room any more.

I've tried many different headphone amps, but as others have said, can't really make a good recommendation without a budget. There's decent $100 ones. There are awesome $10K ones. And a whole lot in between.