Upgrade my CD player or futile effort?

I have a Linn Mimik II and a Quad 99, both of which give my LP12 good competition.

Yeah, I have a Rega Apollo and a Schiit multibit DAC. Sounds wonderful! Very ‘analog’ sound. I also want to hear that Denefrips DAC. Invest in digital and it will sound fantastic. 
Sam in Massachusetts 

While a better DAC R2R ladder will help you, if you can rip all your CDs "bit perfect" into a computer and store them on a USB flash drive with a backup copy and play the flash drive through a streamer such as a Bluesound, it will not be as difficult as you think. You might even eliminate the use of the CD player. I did this with my Bluesound Vault 2i and use storage on a flash drive because that is the only way I can index my collection by composer's folders rather than by "artist and song." I stream free radio stations from anywhere in the world especially if the atmospheric conditions weaken the antenna signals from distant classical stations for my Magnum Dynalab FT 101A FM tuner.

Hi, After all I read here! There are many ways to go! I have ran the gamut of using a lot of stuff! From Dac's and Transport to highly modified CD players! The best overall sound was definitely switching to tubes! Like others have said they liked the Dac's with tubes! All you invested into analog and nothing into digital,  you really are missing out! I had a 2 piece Dac with a Levinson 31.5 Transport! The inner detail was spectacular but still not smooth like analog or tubes in  CD system! I now have an Ayon CD Tube player and it is Fantastic! Not Cheap but with top load Transport and tube Dac's! Sounds like analog without any noise! I'm an Audiophile from way back and always recommend tubes whenever possible! So if you want to hear unbelievable CD sound! You can! Also, less can be more! By bypassing my pre amp and running directly into my mono tube amps! Less Connections the better! I also recommend and use Solid Core Speaker  Cables and Interconnects! Goodluck in your search for better sound!

Well, it has now been 10 days since the Denafrips Ares II has been run continuously on full power as recommended. So time to give you my final impressions as to the Ares II / Marantz CD6005 combo. First off running the Marantz through the Denafrips is like driving your car after cleaning the windshield. The veil being taken off image being way overused 🙂
For sound testing comparison, I only used vinyl I purchased that came with a CD included so there is no chance of getting a different mastering.
I used Pain of Salvation -Entropia, Riverside - Wasteland, Robert Wyatt - Shleep and UMG - Death of stereo. Rock is what I listen to 90% of the time, so this mix of soft jazzy rock to hard prog metal covers my range well.
I played songs from each of these records back and forth multiple times from my analog source to my digital one. I am happy to report that my digital source, costing about a fifth of my analog one, is now basically on par with the analog source sound wise. It is slightly different but not in a bad way. The digital offers a more defined space. Not wider per say, but better displaced. Like sounds coming from outside the speakers are better perceived. It definitely gives a little more clarity but without being harsh on most records. I repeat that I will only play the Denafrips on NOS setting. No OS for my taste.
The digital bass is also deeper, definitely more pronounced. Since all recordings sound different, I would give the nudge to analog for metal since it can lean harsh sounding. The analog definitely tames that down more than the NOS digital setting. However I give the nudge to digital for anything dark sounding. It's like replacing a 40 watt light bulb with a 75 one. On well balanced records I honestly can not prefer one over the other, and I tried. One thing I appreciate with the analog rig that I can't control with this digital setup is the phono preamp gives me the option to tame down bright records with setting it all the way down to 60 ohms as necessary. In my room I like it best on 475 ohms which gives me the clarity and wide space I like for most records. On the other hand, the Denafrips can only go brighter with the OS setting. Once you got it on NOS, it's as tamed as it's gonna get.
In the end, I do now realize the true value of digital which many analog fans on this site discard. There is no doubt that I could probably better my digital rig if I put in the same money that in my analog rig. However I won't do that since I would then have to upgrade my analog 🙂
Not that much of an upgrade fanatic.
Very happy with my digital now that it is basically on par with my analog. Highly recommend going down that road to ones who may contemplate buying CDs. With over 2,000 vinyl and less than 400 CDs, buying CDs is what I am going to do for a while. Huge plus since so many newer recordings never make it to vinyl. Life is better with music. Thanks to everyone who tried to help here.