I’m a “neutral head” who has long owned the HD 600 and explored upgrades.
Common recommendations might include the Focal Clear (Original) at $1,000 or so, Clear MG $1,500, Sennheiser HD 800 or HD 800 S ($1,100 to $1,400 street; varies per sales and discounts). In the price-is-no-object class, the Focal Utopia ($4,400) is a logical contender for mastering. However there are many esoteric $5K models out there that I haven’t tried. Check out @Resolve’s headphone ranking thread for opinions and reviews based on greater experience.
The Focal family offers dynamic, clean, and punchy sound with better treble extension and detail than the HD 600. However, the stage isn’t very wide (but wider than the notoriously narrow HD 600).
I’m currently bouncing back and forth between the original Clear and HD 800 S, and find the HD 800 S better in every way except dynamics. Its tone and timbre are similar to the HD 600, but the treble is much more extended and relaxed. Its stage is among the widest available in headphones. However, the bass isn’t deep or punchy, so I routinely use it on a tube amp or with EQ. The Clear is easier to drive and not as picky about amps, but the mids are relatively grainy and the highs can be edgy on some setups.
In my experience headphone ROI/value absolutely increases to the $1K to $2K range, but the law of diminishing return bites after that. I’ve demoed $5K to $10K systems but not felt compelled to buy. Still, many others on this forum do indeed prefer these products, and I too hear differences. Everyone’s hearing and priorities differ, so in the end you must try for yourself.