There is only 1 case that I can think of that would allow both flatness and louder highs, and that would be: DEQ
Where you limit the amount of boost to the ULF, so that it is flat at lower SPL's, and as the SPL increases... the system becomes more and more mid-bass heavy as the ULF boost is automatically deactivated.
To my knowledge Velodyne has used this extensively for the last 20 years, and now even SVS and several other DSP-equipped subs have this sort of thing too. (It's almost expected these days... in fact.)
In DIY subs it is less common, unless the person knows about it, has the equipment to implement it, and chooses to implement it.
I know I do, and a few others have said they do as well...
A lot of subs just make-do with a HPF and a limiter, no DEQ is ever applied, just PEQ (if that) and that is noticeable when they get tested since the mid-bass is of equal-loudness up to the natural limits of the sub's ULF, as explained above. (So they never use the full mid-bass capability of their subwoofer system.)
Signal limiters, power limiters, and soft-clip limiters (and/or actual clipping) will ultimately limit even the amount of mid-bass that is possible (thermal-compression of the voice coil will too!