Someone needs to take a leap of faith and reinvent the wheel with something new. I think something like resonance and Q factor could come into play. Its hard to do, there's only so many ways to cut, boost, passive cut, shelf, and bandpass our narrow bandwidth. But I believe there is something out there. Along with resonance, it would be nice to have a "EQ" that you taylor specifically where in the bandwidth your signal breaks up, and how much it does so.
Imagine being able to just make your signal break in a certain range, and then also be able to raise and lower the amount of breakup. Go even farther and change the type of breakup. THAT would be nice, not for everyone and all the time, but different, and useful. Ive built a similar plug-in for my DAW, but I wouldn't even imagine where to start with real hardware
Pretty sure the (out of production) Iron Ether QF-2 would fit most of this functionality. I found one on the classifieds here a couple months ago but I haven’t had a chance to really dig into it yet - it’s a pretty overwhelming pedal admittedly.