I realize I may be killing a sale of my HE-400se here, but I don't want to steer you wrong, either. If classical and film scores are your jam, I recommend the Focal Elegia, a $900 closed-back, dynamic-driver headphone on sale for $379 at Adorama:
https://www.adorama.com/fofelegia.html?sdtid=15265996&emailprice=t&sterm=RgEShb2OCxyIW::z-U1k-y9GUkGxFZWUN24E3w0&utm_source=rflaid62905
The Elegia are a mid-fi headphone, and the difference from the HE-400se or the HD 6XX is apparent. Better detail and separation, for sure. Better tonal control. Also much easier to drive than the HE-400se or the HD 6XX. Oddly enough, the closed-back Elegia also has better soundstage than the open-back HD 6XX, which has a detailed but narrow stage. In summary, I would say the stage of the HE-400se extends past your neck, reaches the edges of your ears with the Elegia and never leaves your head with the HD 6XX.
That said, the Elegia are nearly three times more expensive than the HE-400se (four times more if you buy mine used!). And they're really not the greatest all-arounders due to their less-present bass and mids- and treble focus. The bass is there and punches when needed but otherwise stays in place. I don't use my Elegia for rock or EDM, but they're lovely for stringed genres I like, such as folk, alt-country and bluegrass, some non-aggressive jazz and vocals.