Actually, out of the HD6xx series, a reasonable option in regards to better sound-stage and overall value would probably be the HD6XX from Massdrop.
It's probably better, even marginally, in terms of sound-stage and sound profile compared to the standard HD600.
But again, might not be worth the move if you're only after an improved sound-stage over the HD599.
Also, it depends what music you'll be mostly playing.
In my view, good recordings of most pre-90s music (especially 60s-70s stuff) can be a better match for the HD599 (straight, without any EQ).
For 60s-70s blues/soul/funk and classic rock in particular, width and depth of sound-stage are a serious bonus.
With music like that, the HD599 can offer a more realistic rendition with a better sense of flow or 'musicality'.
Again, always compared to the reference-standard HD600, without EQ.
More or less, I find the humble HD599 performing closer to a set of near-field speakers in that aspect.
Apart from the aforementioned HD6XX/HD650, other possible alternatives that might offer a similar rendition and hopefully an improvement in those areas, could be the Audio Technica ATH-R70X, the AKG 712 Pro and possibly a candidate that i don't see discussed very often, the Shure SRH1440.
Any HD599 owners out there, fortunate to have any of the above pairs in their collections please feel free to add your own experiences.
It'll be appreciated.