A DAC to help overcome compressed music?


I have found after upgrading my system, to a much higher level then I ever had before, that with some of the music I enjoy I can now really hear how compressed the music is. I could always tell, but now it’s really obvious to the point of wondering what I can do about it - from a digital source perspective. Would perhaps a certain type of DAC or DAC’s that have various different settings as some do, help “improve” the compression in some way? Or do I simply need to live with it? I am sure there are many others that have had this happen to them. I use a Bluesound or Qobuz currently. 
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I was not specifically looking for a DAC. I was overall looking to improve sound of some favorite music that, as another poster mentioned, was purposely recorded a certain way to sound “good”for lower quality sound systems. Which ends up sounding pretty bad on a better system. That being my quest, if a better DAC would do it, so be it. However, perhaps I should keep another system for that, one of those 80’s receivers, Bose 901 or Cerwin Vega speakers or some such (jk). 
Agree with the other posters here.  If the recording is damaged at the source—badly compressed recording—there isn’t a fix.  The irony, as the OP is discovering, is that as the rest of the system improves, the defects in the recording become more obvious.  I recommend listening to the badly compressed stuff with a $50 Bluetooth speaker because it hides more of the warts and you may enjoy it more
I seem to recall that many years ago DBX made a CD player (DX5?) with processing features that claimed to do what I think you’ve seeking.
I definitely do not recommend it, but a preamp with a high 2nd order distortion profile like Primaluna will give you an added sense of depth/space but even then, compressed dynamics will still be present and it would be a case of the "cure" being worse than the disease.