You might be disappointed with the results in that price range when pairing with the Empyrean. Consider saving up and getting something in the $2000+ range. Headphone and headphone amp matching can be somewhat tricky but when you put together a $3000 pair of headphones with a budget amp, it’s not going to sound all that good, even with ones as easy to drive as the Empyrean.
A friend of mine tried to discourage me from buying these headphones last summer, saying that they lacked that last bit of resolution. At that point in time I would have agreed with him if I was comparing their sound to something like Warwick Acoustics Sonoma M1. At the time the Empyrean were powered by Sony TA-ZH1ES. It’s a great amp but not top of the line. The results that it produced were great in that price range but one can do so much better if funds allow it. Now, the Empyrean powered by the Chord Dave is the sweet spot for me. This pairing can easily beat some well regarded electrostatic heavyweights.
I'm going to have to push back on this one. The DAVE looks fantastic, seriously, Congrats!
However, a person certainly doesn't need to spend anywhere near that money to enjoy some great sound on the Empyreans, and it's not strictly a matter of how much you spend. There are phenomenal DACs, AMPs, and DAC/Amp combos that I've heard great things about on this thread and other places for well less than $5k USD, some less than your 2k mark, and some, like my Topping DX7 Pro, may be well under a grand.
The Burson Conductor 3XP, for example, is not unreasonably priced for what it is- and is obviously less expensive than most of the Chord Products: Dave, TT2, or Qutest (stand-alone, even without amp), and it's substantially cheaper than the Sony TA-ZH1ES as well. The Burson may simply be a better match for the Empy than the Sony. That SINGXER SA-1, with the right DAC, may sound great as well, I'd be eager to hear it. Or how about the Flux FA-10, or something like that? There's some great value choices out there.
The Empy is a well known for a warm, smooth presentation, and so plays well with analytical, clean gear for many people, and a lot of clean but analytical amp/DACs like my Topping are very reasonably priced, but may simply be just too analytical/bright for other TOTL headphones. That's a major selling point of the Empy, not a bug, but a feature. It's not just about being hard to drive, it's about being easy on the ears while still being resolving. That's by design, and is at least one reason why I bought the Meze Empyrean in the first place.
As I've said before, for me, my Elexes with DX7Pro is not even a comparison to my Empys with the same Topping (other than punch and slam), and I seriously doubt the next Focal up, the Clear, would fare much better. As laid back as the Empy is, and as treble forward as the Elex is, the detail retrieval is just not even close, and if I A/B I have absolutely no difficulty hearing EXACTLY what I paid the extra money for with the Empyreans, and all in a very effortless, and for lack of a better term, natural way.
Based on my experience so far, I would firmly opine that the choice of headphone remains the most important part of the equation, and by no small margin. As such, I have to disagree and say that it's perfectly sensible to buy the Empy and build around it as you go. Not that anyone needs our permission.
If/when I do upgrade from my DX7 Pro, I'll come back with a honest assessment and let you know what I think. Right now I'm just saving, and eyeing anything from the 3XP to a Qutest/GS-X Mini Combo, maybe even a TT2 when the time comes. But by no means do I feel that I am doing the Empyreans a disservice by driving them with my Topping in the meantime.