Looking for suggestions

I’m looking for some help in upgrading the "digital" portion of my two channel audio system. I have an average quality CD player and a Bluesound Node 2 used exclusively for wireless streaming of HD Tidal content. Some say the DAC in Node 2 is decent but I can do better with an outboard DAC. So I guess, I’m looking for a product that can improve both the quality of CD playback and the Node 2’s streamed content. Can this be accomplished by buying one good quality DAC and feeding the CD player and Node 2 outputs into it? I could also get something like a Musical Fidelity M3scd which is a CD player and a DAC - a much better CD transport than my old CD player, but my preference is to keep the cost below $1K.

Any suggestions? Thanks.

Added - Opinions on MF M1DAC welcomed.

Yes, a single DAC with multiple inputs can improve your current CD playback and streaming digital. For $1000, I would stick with a DAC, not a CD player with digital input. Reason is the DAC/digital input will likely be an after-thought on a sub $1000 CD player.

That said, I do own a nice CD player with multiple digital inputs. My Rega Saturn-R is an excellent CD transport/player and it has 5 digital inputs. But you can't yet buy one used for $1000. They are currently closer to $2000.
No one believes me, but the little Parasound Zdac v2 is quite a performer and in your price range.