Wanting to narrow the field for compatible speakers

Hi

In your budget I would consider kef blades, magnepan 20.7 or 30.7, avantgardes or acapella horn speakers. Still a young audiophile, yet to push the boundaries to discover all that is possible, but from what I know these are good stuff!

Regards
Ben

Have Eric build you some Ulfberhts with all Be tweeters, Duelund caps, Goertz inductors, Path Audio resistors, and Kimber 4TC. There should be plenty left over to put them on Townshend Podiums. Put all those other speakers to shame. To shame.

Eric is at this very moment reading this, smiling and nodding and saying, "Yeah, they would."

What improvements/changes are you looking for?  New or used?

I would echo @soix questions and would also be curious if you can tell us a bit about what you like in terms of sound.  There are a ton of speakers available in this price range and the speakers you have are not exactly mediocre.  For example:

Vivid Kaya 45s
Avantgarde Zeros
Wilson Benesch Vectors 
Stereokonzept Model 2
Perlisten S7t
Raidho X2/X3 or C1.2
Vienna Acoustics Liszt
Canton Reference 2K

These are all radically different sounding speakers that are on (or near) your budget and will sound and look very different than what you have.  I could probably come up with another 20 different speakers.

What I can't say is that any of these is inherently better than your Sophia 3s, just different.  I love all of these speakers for different reasons.  The question is, exactly what do you want?  Are you open to adding subwoofers?  How do you listen, dB level, focused or are you up and about?  etc...