Recommendations for headphones under $400?

Good questions!
Wired for sure, will be used in a couple different systems
One is an old Linn Classik all in one with built in headphone output
Another will be from a Schiit Magni 2.

Mr Speaker's Mad Dog's. Nice rich sound. Probably not as accurate as my up market Senn's but very enjoyable.

Sennheiser Momentum's do a nice job, AKG and HiFiman

Lots of good options at $400 or below, actually. One of my go-to pairs for rock and pop at work is the PSB M4U 1 (which I pair with a dragonfly red). As far as performance for the price it is an excellent choice. Great options at the high end of this price range and with ample bass are the Master & Dynamics MH40 and the OPPO PM-3.

Yes I know there are LOTS of options at this pricepoint, that is part of the problem...lol.
I really do not know a great deal about headphones, by that I mean the names and models that are the best.
Sennheiser I remember having numerous pairs back in the 70,s and 80,s and thinking were excellent value for money at the time.