The next step up would be the DCA Stealth. MSRP is $4k. Used ones can be had from $2800 to $3200. Very similar sounding from the midrange to treble. Somewhat less response in the bass region but the clarity is unmatched. It definitely requires some power to push the volume but the HPA4 should be able to handle it.
The AKG K371 and the DCA Stealth are tuned to the Harman target frequency response curve. If you like what you hear, try to find other headphones that measure similarly.