I had an LCD-2C for several years and loved it. I agree with
@xTelepathetic that the Aeolus could well be a great contender, although I've not heard it for any decent amount of time or in a good environment (twice at CanJam). I found it a bit too warm for my taste, and without enough top-end air. It didn't sound as open or spacing in its staging as the LCD-2C, but then I didn't necessarily hear it with the best gear or with a mesh and pad combination that worked for me.
The closest I've heard to the 2C are the Atrium and Caldera, although both need to be set up the right way. The Atrium is much more forward in the upper mids than the 2C, too much so for me, stock, so my pair has the solid mesh installed on it (and the Universe pads), which makes for a lovely dark tuning, one that's closer to the 2C. The sub-bass isn't as robust as the 2C's, but the bass otherwise is outstanding - rich, textured, punchy, and with plenty of slam. You also get lovely timbre and great, strong and gritty textures from the Atrium, though not quite so crunchy, gritty, or growly as the 2C when it comes to rock guitars. This was one of the stand-out qualities of the 2C for me.
The Caldera I heard in my system for about 5 days and, again, it needs the mantle mesh and the right pads (I'd suggest the stock or the thick Caldera ones) to get the darker tonality. Its bass goes deeper than the Atrium's, and bests the 2C's, although I didn't compare them directly (I'm going off memory here). The mids are more even than the 2C's, without the upper-mid recession (here the mantle mesh helps get the Caldera closer to the 2C), and the treble provides the same kind of air and sense of open staging as the 2C. The Caldera excels, like the 2C, at presenting rich textures, and is better at recreating the crunchy, growling guitars of the 2C than the Atrium. So, Caldera wins for bass and for gritty textures.
The Vérité Open has the clarity you're after. Its bass is excellent, not quite as deep or robust as the 2C's, or the Caldera. The VO has a laid-back tuning, and while slightly dark, it does have more energy in the treble than the 2C, especially around ca. 6 kHz (I think), which makes for a difference in the sound sound vs the 2C's. I found the VO to have a bit more of an edge to it - and to be a bit more fatiguing - than the 2C, but then the 2C is one of the least fatiguing headphones I've heard, when properly amped. (To be clear, the VO isn't bright or inherently fatiguing: I'm sensitive to certain frequencies that the VO might excite, and many find it to be absolutely free of fatigue). The clarity of the Vérité is wonderful, though, so it's well worth checking out, if you can, to see if you like it.
The Auteur Classic is very different; it's brighter, closer to neutral, and has many qualities that differ from the 2C.
I hope this helps! At the risk of stating the obvious, if you can, see if you can audition them at a meet or at a Canjam before buying, and failing that, I'd suggest buying used pairs so you can sell them for less of a loss if they're not to your taste.