Honestly, what you will notice is what people call diminished returns. The reason I have this highlighted is because it is entirely subjective in this hobby, but not so much in others. The differences between headphones and amps gets less and less as you move up. Feel free to experiment and see where your comfort zone is.
An example I can give you is my own - a few months ago, I got a chance to try out a set of STAX headphones (SR-407 with the SRM-252S Amp and HeadAmp Pico USB DAC). I only really had a my pair of SRH 840's to test with. To give you an idea how big of a difference in budget this is - 840s are half as expensive as the amp or the DAC and about a third of the 407's.
I was expecting to be blown away. I was thinking that as soon as I put them on my head and started listening to music (all high quality FLAC recordings, don't worry) that the music would feel different. I was severely disappointed. In all honesty, they sounded like my pair of SRH 840s except that it was open. After about a week of owning the set and listening with it, I finally got a slight glimpse as to some of the differences between the headphones. These differences though were so minor that it made me lose interest in the high end side of this hobby. I realized that just because something is more expensive does not mean it's automatically better for everyone. For me, that setup was way too costly for the minor differences it provided.
I now have a pair of DT 880s and Mad Dog 3.2's with a Schiit M stack. I think I'm fairly set for the next few years now.
tl;dr Tried a high end set-up with high expectations. I was disappointed and now am sticking to stuff I am comfortable with financially and sonically.