I’ve had as high end a headphone system as I could afford for nearly fifty years. I got serious into digital (sources for my headphone system) about fifteen years ago. I went through a dozen headphones, and amps, and sources. Given where you are... I would say your headphones are plenty capable.
The primary determinant in the sound is the headphone amp. Headphones vary in requirements tremendously. But respond really well to massive power. As I said, I have had many head amps. My system got tremendously better when I found Woo headphone amps. Lots of natural musical power. If you start with a really good powerful headphone amp... your headphones are going to sound incredible... then you can add other improvements. I have a Woo WA5... it simply took my system a couple levels beyond where it was... and it was already very good by nearly anyones standards. I would get the best Woo head amp (not WA6... too little power) and a BlueSound streamer. That will improve your system by and order of magnitude. But go all in on a great head amp... I spent thousands on different high end headphones and different amps... one can save a lot of money by one bold move. You can fool around spending lots of money and not get there.
You can see my headphone system under User ID in virtual systems. I replaced the stock 300B tubes with Takitsuki ($1K each... incredible... but later).