I have had a headphone system for decades. Over the last ten or fifteen years I finally buckled down to really make it great. It took many years. I went as far as importing a headphone amp as well as buying several others. For headphones the most important component is the headphone amp... period... OK, within reason not a $25 steamer with it.
The company that changed my perception of what was possible was Woo. They specialize in headphone tube amps. I purchased a WA6 (fantastic but limited power), then the two component WA6SE (fantastic but a bit more power... but limited) and the lots of non-Woo solid state headphone amps. Finally I bought the Woo WA5LE. That amp (see my virtual system) completely changed everything. It is so powerful as to be able to power speakers, it is a 300B tube amp, so is incredibly warm and natural. The combination takes any headphone (especially Sennheiser) and grabs it and tell it who is boss.The power, natural musical sound that comes out is incredible. I have Sennheiser 800, Focal Utopia... etc. In each case they have never remotely sounded as good... not even close. The amazing thing, is when headphones have this kind of midrange bloom and power... they are satisfying from a power perspective... like a big main system is. When I listen to them, I don’t crave going to my main system to get the satisfaction of the bass hitting my chest.
If you really want to make a leap that will completely change your system. Get a Woo WA5... later upgrade the 300B tubes to Takatsuki. Then upgrade your inputs... each upgrade will be amazing... with WA5 in place.
I seldom say, "get this". But the way you phrased your question, it seems like the right thing.