This sounds like a very expensive trap. Your speakers may already be good enough.
Based on personal experience, i'd say the biggest sound improvements are most likely in the room, not the speakers. Mine are set up in the living room, which i know has too much open space and hard reflective surfaces. There is very little that i could still fix in that space.
With my headphones and dac/amp, there's nothing left to fix. I could buy something else that's potentially better, but that's a different story. Sure, i could buy a pair of speakers 5 times the price of my 15 year old KEFs, but i don't expect them to deliver superior sound in my flawed listening space.
Assuming i had the money and would be willing to part with it, i would build a new house, incorporate a space suited for critical music listening, and then install those Dynaudio Contour 60s 😉. Until then, i accept that my headphones produce better audio, even if the complete listening experience is better with the speakers in the flawed room (and a glass of wine, and company, ...)