I would suggest a used Fostex TH-X00 Mahogany for $200ish and put the newly released ZMF Ori suede pads on it. Make custom attenuators to put inside the earpads which are not hard to do - simple as cutting 2 crescent moon shapes from a manila folder. And if you want to further improve it to near top end level, for a little over $30 you can get a driver frame/housing dampening kit from Lawton Audio which will noticeably improve the detail, clarity, dynamics, and instrument separation (need to specify you don't want he cup dampening otherwise you will get the full dampening kit at $50ish. The cup dampening really messes with the bass in a negative manner - reducing the level and shoving it back physically in the mix.)
I recently picked up a second TH-X00 PH used for $260, which I put the E-MU Palo Santo cups from the recent Massdrop deal on and ZMF Ori suede pads with custom inserts. Not as punchy or hard hitting as my PH pair with the stock Purpleheart cups and Jmoney V3 leather pads, but still WAY beyond the HD6XX in low end with beautiful mids and highs I like better than the 6XX, just as detailed and clear yet more full and dynamic sounding (Foster Biodyna drivers are absolutely lovely to listen to...) Plus you would have one very nicely constructed plastic headphone in the HD6XX, and one with more exotic higher end construction void of plastic (TH-X00 magnesium/aluminum alloy is lighter than most plastics).
Such a modded TH-X00 is a great all around phone, bass tilted somewhat, but with well above average detail and clarity for closed/semi closed phones which works well with pretty much any type music, including classical. Actually fairly open sounding. They sound great from most any source as well, whether straight off a phone/ tablet or connected to a dedicated desktop setup. Seem to absolutely love a high powered Class A amp setup that is warm leaning though - spectacularly rich and detailed experience from it with PHENOMINAL BASS, especiall the detail and finesse in the sub-bass. Would be a great compliment to an HD6XX series. I'm in on the HD58X drop because there's some minor things about the HD6XX I wish changed, which the HD58X seems to have done based on all the reviews of the preproduction units.