would you say your onboard audio quality (the dac) is good? or would you be interested in an external dac such as using the modi+magni stack (or o2+odac, similar)
it would be worth looking at the hd600, hd650, he-400i for good middle priced options or the dt880, dt990, k7xx for lower priced options.
i recommend reading some user reviews
http/www.head-fi.org/products/sennheiser-hd-600
http
/www.head-fi.org/products/sennheiser-hd-650-headphones
http/www.head-fi.org/products/hifiman-he-400i
http
/www.head-fi.org/products/beyerdynamic-dt-880-pro-250-ohm-semi-open-reference-headphone
http/www.head-fi.org/products/beyerdynamic-dt-990-pro-headphones
http
/www.head-fi.org/products/akg-k7xx
on a budget if you want soundstage, bass and bright treble the dt990 has it. they can be a little bright so you might want to eq them down. the 880 is more neutral with less of a v-shape and less treble/bass spike than the 990 has. i dont know much about the new k7xx but from what i've read its a bit bassier and easier to drive than some other akg cans so it may be suitable for you.
the hd600/hd650 is a natural upgrade from the hd598 series with a good soundstage and is more laid back and easy listening than some other headphones. the he400i planar is good all around but does not have a huge soundstage.
there are of course other options, perhaps some of the others could make a few other recommendations.