Can Room Correction Be Added to an Existing DAC?

My dealer is experienced with Anthem and set up the 2 AVRs in my house.  I’ll query him about Dirac vs the Paradigm .  I am also wondering that I should go this route, should I add a sub to the two channel system, because the biggest improvements that I hear with ARC are bass oriented.  OTOH, my speakers are B &W 803D, and they are pretty full range

The MiniDSP SHD Studio is a much more modern component, with much better quality internals than other MiniDSP products. I would say say hardware wise the Paradigm PW Link is in a similar class as the MiniDSP 2x4HD. The SHD Studio is in a different league altogether.

Dirac and ARC are generally considered to be similarly good, with many people giving a slight nod to Dirac. I believe Dirac is much more flexible, allowing you to tweak the target curve to suit your needs exactly.

minuDSP does include Bass management upto 2 subs which is very flexible, but the Bass management part has a steep learning curve.
The benefit of a sub with good speakers is not so much better/deeper bass output, but more of flexible positioning to reduce room modes. I would recommend getting a UMIK-1 mic and downloading REW (a free audio analysis software) to measure your frequency response first, before deciding if a sub is needed.

Most people/rooms benefit from multiple bass sources, so room modes cancel each other. However, In my case my speakers when measured individually are quite flat, However when I measure the combined L+R response with a mono signal, I have all kinds of peaks and nulls in the bass region. Adding a sing sub, introduced some crossover anomaly but restored a flat bass response. With a little tweaking of the crossover, my overall combined response is now fairly flat.

Look into DSpeaker line of products

I had the DSpeaker X4. Good stuff. Easy to use. Built in dac, but has digital out as well. Worth a look, but $$.

As many others have said, you can add a digital signal processor in front of your DAC.
Dirac with miniDsp is probably the most cost efficient solution. If you want to evaluate Dirac you can download a time limited evaluation installation for Windows or MAC.
I tried it and the effect is not mild. The balance achieved is an improvement bot overall I didin’t like that the stereo image becomes too wide, to an extent that I lose the central image.
Also, I own LS50 and tried the Acitve DSP-ed LS50w. I didn’t like the result. I think some detail is lost in the processing.
Try before you buy.