Advice on buying good CD player that will outperform my Primare cd31

Check out JAY’s Audio, 

https://www.vinshineaudio.com/jays-audio

Alvin, at Vinshine, is a great guy but if you are in North America it is a whole other deal. 

I purchased a ps audio perfect wave dac w/bridge and transport for a little under 2000 and am very satisfied. I only had an old marantz CD player hooked up to an old audio alchemy dde v3 + dtiv2 for comparison. The ps audio gear is quite a bit smother and more analog sounding to my ears. On the other hand I rarely listen to it anymore after purchasing a VPI scoutmaster here, but still glad I have it and will eventually get in to streaming with it some day.

Wow, its a TEAC on steroids.. If you get one of these you in a whole other dimension of CD players... 

Opera Consonance Droplet valve cdp is an interesting player and very distinctive in looks and sound. They don’t come up much second hand, and are much sought after so good luck in a hunt for one. 

http://www.6moons.com/audioreviews/droplet/cdp5.html