Sticking with CD's for now

Could anyone offer some help with my interest in adding an outboard DAC to my current Ayre CX7e MP digital player.
DAC would need to have aes/ebu input capability to consider it.
Trying to find improved sound via CD player for the time being with future options the DAC can provide to be considered.
Any direct experience with opinions and options would be appreciated. Price range $2000 vacinity new or used.

I used to have a Mytek Manhatten I which I am pretty sure had AES/EBU

I would look at the Brooklyn to see if it has that input, and if so that is what I would get

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The Yggdrasil with the latest analog output board is around your range and has AES/EBU, USB, BNC and coax S/PDIF. I've got it paired with a transport that is probably close to what you're using (Jay's CDT2 Mk2) and frankly, I don't even turn on the turntable these days unless I don't have what I want to hear on CD. Measurements be damned, it sounds very natural, engaging, and just plain fun. I'm pretty sure someone somewhere measured noise from an Yggy outside of typical human hearing range two+ years ago and "objectivists" cast it aside as defective, but I can assure you, it sounds magnificent to these human ears.
If you can find any area where the two DACs I mentioned fall short, I’d love to hear it. I’d appreciate real descriptions and not “lacks breath”.
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You are the one who stated my recommendations weren’t up to par for the CD player in question, based off price alone; then you go on to recommend a DAC that has 16x the noise+distortion.
Good combos are:

Transport -> Synchro-Mesh -> Reference BNC cable -> Metrum

Transport -> Synchro-Mesh -> Reference BNC cable -> Border Patrol

I would avoid any DAC that has reclocking inside on the S/PDIF input.

These will both realize the benefits of 7psec of jitter.  Customers that have these are extremely happy.

Steve N.
Empirical Audio
Appreciate the responses so far.
Just to reiterate I am interested in adding a DAC with aes/ebu input to my Ayre CD player. Any direct experience or thoughts and recommendations on a DAC that could offer improved performance will be considered.
I had an Ayre C5xeMP and did exactly what you propose. I chose a Holo Audio Spring Kitsune Level 3 DAC which I see has now been upgraded.
The sound was fantastic. I then decided to go on a sole CD transport hunt and sold the Ayre. In hindsight I should have kept it. This DAC is an R2R ladder design, the folks at Holo Audio are very helpful. Read some of the reviews and good luck on your journey.