The Absolute Sound as compared to just sound? re: Headphones.

soix, Thanks for you thoughtful post.  My listening is mainly classic Jazz from the 40s through the 70s and  well recorded female vocals doing standards and Jazz vocals.  I prefer acoustic instruments with an allowance for well recorded electric guitar and bass.  Being esoteric should never be taken as arrogant.  Knowledge and/or experience that is shared is a gift that the reader/listener can accept, reject or modify based on personal experience.  It is done with film and restaurant reviews world wide, and should be no different with most consumer goods.   Having driven race cars at Road America, I understand that is a non-standard experience and perspective on handling and how to drive.....For many "going out to eat" means a place with a drive-up window, but that is not what I consider a dining experience. .......however, there are always Twinkies and Ding-Dongs....for real gourmet foods. 

soix, as a P.S., I have three places I might listen to "phones" with.  A main system with CJ-ART, Magnepan...etc, a 2nd system with a Magnum Dynalab receiver, Quad 12 speakers and Wireworld interconnects and a "for late night/going to sleep" Nakimichi Soundspace 5....which would be the most likely place to use headphones.  With all my systems now and throughout my life, sound quality is my goal, volume has never been anything of interest. 
Perhaps not on this site, but many Americans have a jukebox at a bar as their sound quality standard/comparison.  

Do you have a budget in mind, and do you have the capability to stream music through Qobuz, Tidal, etc.?

Because of most listening being late at night/going to sleep with the Nak SoundSpace 5, I would think under 200.00 and as of now I do not stream.  Thanks for you input.  Jim

Since you’re a Maggie fan I’ll highly recommend the planar HIFIMAN HE400S that I actually own, but they are open back and leak sound that may bother someone else nearby if that’s a consideration.  They’re normally $299 but currently on sale for $249 and I think they’re well worth stretching your budget a little for.  They’re very detailed but natural and open sounding (like Maggies) so there’s a lot of “outside the head” imaging going on and the headphones disappear as a sound source very well also — which I love.  They have the added benefit of being fairly easy to drive, especially for planar ‘phones, so you shouldn’t need a separate amp to get them going.  That said, and like all good equipment in audio, they will scale up with with a better amp and source so you can kinda grow into them in stages if you like.  That’s what I did and am extremely happy with my current setup that consists of streaming hi-res Qobuz through my iPhone or iPad to (via an Apple Camera Adapter) an Audioquest Dragonfly Red portable amp/DAC into the 400S.  BTW, I highly recommend Qobuz that you can try for free, and it’s only about $15/mo. if you decide to stay with it — best 15 bucks I spend every month as I get both hi-res sound and the ability to find worlds of new music on a daily basis (rarely bother spinning discs anymore).

Anyway, that’s just one recommendation FWIW and hope it’s at least somewhat helpful.  Best of luck in your search.