3way replacement for my 2way

I’m thinking of replacing my Triangle Comete EZ Bookshelf speakers with some 3 way speakers and seriously considering purchasing either 2nd hand or new.

My Triangles are good about 85% of the time, they’re somewhat forward, not very forgiving and lack that warm feeling of a 3 way.

My Triangles currently are on the company’s accompanying stands about 24” from the back wall and about 20” from the side walls and towed in projecting to my couch’s center. My room is 12’x 11’ w/ a 10’ ceiling, in addition the room has a tray in the center giving the center an additional 1’ of height. The floor is carpeted, no furniture other than a couch against one wall facing the equipment and record storage racks on the other wall, one window on the side wall is treated with thick room darkening curtains, basically the room sounds pretty good.  

I’m running a Carver Crimson 275 Amp that’s hooked up to a Parasound ZPre3 Preamp. I mostly listen to vinyl on my Orbit U-Turn TurnTable equipped w/ a Ortofon Super OM20 Cartridge stylus that’s hooked up to an IFi Zen Phono Preamp. 

I get that it’s a “Mid-Fi” set up but it lacks some warmth that I feel is a result of my 2 way’s extreme forward output. 

Like I mentioned prior, my Triangles sound great at times, they just always have that in your face high going on, sometimes more than others. 

I’m looking for 3way speaker recommendations in the $2k - $3k Ballpark that have a nice balance of Highs, Mids & Bass. 

I know there’s some really great speakers out there and not to sound obnoxious, but please don’t recommend some great pair of used speakers that even if I spent six months full time searching the internet I won’t be able to locate. 

Not into Klipsch,No B&W’s or Polks. My music tastes are Blues,Jazz, Big Band, Reggae & Classic Rock if that helps. 

I’d love to hear your thoughts.