[RBNYC2]

I currently own the Little Dot MKIII, which I have done some tube rolling with, and although it was a great buy for the money, I've gotten to the point where I am a bit bored and am looking for better sound. I'm wondering what kind of increase in performance I could get by upgrading to a better amp, and what price point I would need to jump to in order to achieve this audio quality? As far as my budget goes, I'd like to keep it in the 500-800 range, but flexible. I looked at some Schiit amps, and the prices seemed pretty good, but I'm not sure how much of an upgrade any of them would be because I have no means to compare. So, any recommendations/comparisons to what I have now would be greatly appreciated. 
 
My current go-to headphones are the Shure SRH940, but I am also in the process of auditioning others that I may use, so I'd ideally like something that is versatile and can pair well with a variety of headphones. 

 

[Papander]

Umm why not get better headphones instead of spending all that money on just an amp?

 

[RBNYC2]

I've heard a decent amount of headphones, and I think the SRH940's are very good. I haven't found anything that I like a lot better yet, without spending 1k+. However, I am also looking at other headphones--possibly an orthodynamic pair. That aside, I think a better amp might make a significant difference. I find that the little dot is a bit lacking in power because I usually have to turn the volume dial up very high to get a decent output. 
 
Also, if there is something good for cheaper than the range I stated, I'm more than happy to spend less if I can.