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

Once I demoed the Sophia 3 with a musical fidelity A5 (solid state integrated amp) back to back with a $30k AR tube pre and amp (model?). The tube setup lost most of the dynamic bass slam that I found intriguing on the A5. The bass had crazy slam and power on the A5 in a very large room. 
Maybe try a cheap use solid state amp, even a class d just to mess with. If you like it sell it and get a good solid state amp. It is alway a compromise somewhere though. Expect highs to suffer.

I guess I just need to audition a high-powered SS amp and a (sealed) sub in my system. thanks for all the helpful responses, especially from people who have experience with sophias.

I have Wilson Sasha 2 speakers and also have had some issues with tube amps and bass control. I think that you received some great suggestions, including adding a subwoofer, using a loudness control,  and trying a more powerful tube amplifier.

It probably is my bias (pun intended) and the type of music that I enjoy (violins, violas, and strings) but solid-state amplifiers are not a good solution for me. I  recently tried a Luxman M900u ampilifier and a D'Agostino Momentum S250 amplifier, and although they were both great, I could not live without the mid-range timbre provided by a valve amplifier. I now use Audio Research 250SE monoblocks along with a Luxman CL1000 preamplifier (and an Esoteric X-01XD SACD player).

The Sophia 3 has a woofer damping resistor under a cover plate at the base of the speaker. Changing this resistor to a higher value will reduce the woofer damping and allow it to produce a fuller bass at all volumes. Not sure about Sophia 2 or original. Worth it to check.

It should look at PASS 350.8 great bass weight and definition.