I highly recommend investing in a better headphone amp. I have at least five different pair of flagship headphones. Including Sennheiser HD800. All the different headphones sounded different with different strengths and weaknesses. Then I got a truly great headphone amp the Woo WE5 and then put Takatsuki 300B tubes in it. OMG. For the first time ever (after a dozen amps... over decades) the sound quality improved by and order of magnitude... then suddenly the Sennhieser HD800 quickly found there way to the very top of my play list. The Focal Utopia, and Denon, Ultrasound, Beyerdynamic... just fell into disuse. The difference was incredible. I only use the HD800’s now, often for an hour or more a day.
Very often preamp headphone output is a second thought and even on incredibly expensive preamps is not very good.
You can see my system under my USRID in Virtual System. But for decades I tried to make my headphone system as satisfying as possible... I imported a high current amp from Germany... etc, constantly tried new top of the line headphones. It was the head amp from Woo that finally made my headphone system as satisfying as my main system I can listen for hours... the physicality of the bass... the delicacy of the violins or voices. The Sennheisers are world class.
Over time I found a headphone system is like a main system. The headphones probably will cost less than your main system speakers. The electronics cost should be about 80% of your headphone system.

