How does my MF A308 compare to modern integrated amps in the $3000-$6000 range?

Are more recent amps in the $3000-$6000 range superior enough to warrant an upgrade?
Thanks. I’m happy with the sq, but I have no frame of reference regarding other options.
I'm with @jjss49 

Mostly what you'll find out there will only be different, not unequivocally better or worse.  Unless there's a particular aspect of your sound that's lacking and needs addressed (and is easily attributable to amplification), I wouldn't start a new search. 
If you do start wandering, I'd try to start sampling totally different typologies (e.g., a full tube integrated, a class d integrated, an otl) rather than just sticking with other class a/b amps. You'll learn more that way.

And as always, amp to speaker matching is an essential and hard to fully predict challenge.
op did not disclose, but with his good amp, if he is trying to improve overall sq, he should look at source or speakers (assuming room setup is done properly) for areas of substantial improvement for more $ spent... that is where there will likely be more leverage
Just my 2cents worth.

I went from a Musical Fidelity A5 integrated (which I absolutely loved for years and years), to a Luxman L-509X - and it was a definite upgrade.

I got the Luxman used for just over $6K and thought it was worth the coin.

Improved sonic textures and tonality, more features and those meters! :-)
Thanks, everyone. Erik: what speakers do you have? I feel that my MF is a good match with my ATC’s. Obviously, there is a synergy here, let alone all the other factors that others have mentioned. I’m sure it’s true that I need a better DAC, and other elements in my system also need upgrading. My question is more a curiosity thing than the next thing I need to do to upgrade. Following the rest, it’s something I might or might not face.  And it is  nice to get validation that I have something worth hanging onto.

I also have ATCs; SCM11v2s.

I also really liked the MF/ATC matchup, but the Luxman is even better.

But only you can decide if you want to try something different.

I like to buy used (here or other sites). That way I can try gear for myself and flip it back at little/no loss if I don't like it.  
reminded of op having atc’s only thing i would add is that mf’s are voiced a touch lively - crisp and clear sonically

atc’s need all the power and control of a strong ss amp for sure, but they are also ruthlessly revealing of what is being fed to them

so unless op likes a somewhat sharp, ’crystal clear’ presentation of the music, a sweet sounding dac may well be a smart upgrade... one that has a more full bodied, organic presentation like an ayre codex, mhdt, audio mirror or neko audio etc etc
Thanks for the DAC recommendations. That’s a real frontier realm for me.
I do generally like clear, sharp, revealing, detailed sound. I’m not sure why. It could be because I haven’t had the opportunity to hear the alternatives much. All the really good systems I have heard have been detailed.
Basically, my system is clearly way beyond good enough for the purposes of listening to music. My posts here are mostly musings and expressions of curiosity simply because I find that fun.
I also have a MF 308 integrated and have always been happy with it. Some years after it was discontinued, I had a conversation with MF manufacturer's rep for the US and he told me that many considered the 308 integrated one of the best sounding amps MF had produced to that date. Also, he used one for his personal system and had compared it with other amps, but had no desire to replace it. As long as it is working properly, it's a keeper.

I have an older Tri-Vista integrated. Different animal than your 308 but I'm sure similar in some ways. Mine really benefited from a silver conductor power cord. Injected some real verve and jumped everything up a notch.