Can you improve the 'sound' of the Tyler's? Absolutely, but they aren't that bad and unless you have some specific goal you can do a lot worse for more money. I had a problem, I had a goal, and I moved up successfully. But, when I bought the Tylers, my goal was more asthetics than anything else and the urge was to get something new. Frankly I succeded and failed. The Tylers looked better, but overall their predecessors sounded better. And the sound was more important to me.
IMHO, you need to develope some specific goals. Don't buy new amps if you think the Tylers are leaving. Don't buy new amps unless you have a problem with the Tylers you want to correct and you are reasonably confident you can do so. OR, if you plan to get new speakers (out of curiousity) then be prepared to get a new amp to compliment your new speakers. What you have may not work to your satisfaction.
And, if you just want to up-grade something, just to do something (which we all do sometimes), spend your money on sources and/or a pre-amp, tubes or SS depending on your inclinations, which could easily survive the ultimate purchase of new speakers and amps.
FWIW, I never buy new speakers without assuming first that I will be getting new synergistic amps as well. It always seems to work out that way.............:-)