Speaker upgrade question.


Hi all, 
I haven't been here for quite a while as I've been happy with my KEF Reference Three-Twos driven by a Musical Fidelity A308. They're both vintage but they sound great together and fit my somewhat weird room. I'm pondering spending some bucks in the 3-6K range for new (used) speakers and I have a few questions. Thanks ahead of time for anyone who's not too busy to help.
First, would I be  upgrading beyond what my amp is capable of keeping up with? The MF is fairly powerful, but I'm not sure of its limitations since they don't show up in my current system.
Secondly, how high up the price ladder would I need to go before I'd find speakers that offer an obvious improvement over my KEFs to most ears. There would be little point to pony up money for a comparable sound, however much I subjectively prefer subtle differences.
Finally, for reference purposes, can anyone tell me how the following modern speakers might compare or contrast with mine? (Some aren't in my price range, I know) Triton 1R, Kef R7, comparably priced Monitor, Revel, Gato, Paradigm, etc. I wouldn't mind a bit more punch and a bit more bass than I have now, mostly just to experience a different sound - I respect the KEF signature sound.
I know that sometimes it's hard to accept the premises of these types of questions since such matters are so subjective and a lot of folks like to lobby for their favorite brands. I guess I'm not seeking advice about what to buy. I just want to understand the benefit to me of more modern speakers. It's quite possible it makes no sense for me to upgrade.
Thanks again.
Marc
128x128m669326
Yes, I get that a better DAC would make a bigger difference than what I'm proposing, That makes sense. I'm less sure that my amp end up as a weak link.
And thank you, Daros,  for sharing your experience. Your situation is exactly what I'm trying to head off by posting here. I could easily spend a bunch and get worse or comparable sound, especially since I am no expert about all this. I've heard very few systems; i just read a lot online.
In its day, my speaker was very highly rated by both experts and consumers. I know the tech has moved on. What I don't know is how much the sound has.
A realization: I think I'm hoping to get talked out of upgrading, either by people lauding what I have, discussing a lack of progress in sound evolution, telling me my room is hopeless, or pointing out my cluelessness and the likelihood of me doing something foolish.
When money comes in, I start brainstorming what to do with it, and music is one of my top life priorities.
When I'm doing this type of research, I don't consider it "upgrading." It's brining in a different sound. I don't necessarily want my next speakers to sound better that what I have - I want them to be great in a different way. I'll listen to the new speakers for a while and when I want to change it up, I'll swap in the first pair. For this reason, I think it's helpful to have more than one pair of nice speakers on hand if possible. When one gets the speaker upgrade itch, just swap in the pair you haven't listened to in six months.
Sorry for all the posts today. I've got time on my hands.
What about adding a KEFKube sub to my current system? A dumb idea? I only listen to music. Would this change what I hear in any significant way? Would it be a hassle (like last time I tried this with other equipment)?