will changing to solid-state make the bass in my wilson sophias better at low volume?

...I wanted to clarify and add on a bit more to my previous post. 

I initially listened to the Sophias with all those amps without the subs with great bass impact.  

I had listened to my previous floor standing speakers with B&K and Parasound amps and always felt the Classic 120s provided better bass response.  

I know this is a sensitive subject and many are adamant that solid state will always provide better bass, but I believe my ears and regardless what the specs dictate the bass from quality tubes amps is beautiful

I still have the same recommendation but you know....YOU are curious.  Go ahead and find a used solid state amp here on Audiogon that meets your criteria and check it out.  Maybe your ears will like it better!  If not, resell and then you will feel better about your Cary amps and be able to put that to rest.  The seed is planted so if you are like most of us you won't be able to let it go until you actually get a solid state amp in your system...and that's half the fun!  That's what we do, right??  

Have fun!!!

Try improving  speaker position.  Follow the WASP system. If that fails consider amp change. Maybe try Pass Labs 

Darko's A500 Review notes a setting that tilts Highs / Lows at low levels.
"  Buchardt’s ‘Low-level Enhancement (LLE)’ corrects for the Fletcher-Munson effect where, at lower SPLs, our ear-brain is less sensitive to low- and high-frequency information."
https://darko.audio/2020/09/a-long-film-about-the-buchardt-audio-a500/

let's worry about the mids 
in the speakers first. 
   Let's get that right 

Loudness contour adjustment. This is not a fault of your equipment but a result of what is referred to as the Fletcher Munson Curve.

At lower levels the 3k - 4k range appears louder than the other frequencies especially the lower frequencies. This is just part of being human and physics...

A loudness contour control adds the appropriate amount of EQ based on the level you are listening. Most notably at lower levels you need a 10dB boost on the low end frequency to make everything sound in balance.

Best,
Drew