The background is that regarding high gain ss distortion, many guitarists, including myself, find the built-in distortion better than of stompboxes (more alive, roar, less dirty though high gain ...). I conclude that the cause is the supply voltage. Opamps in amplifiers are fed with +-15volts. Clipping is done mostly at diodes (leds/si) and less at opamp itself. Contrary, stompboxes supply is +-4,5Volts, pushes the opamp to rails quickly and clips deadly before the signal reach at diodes. No doubt how dirty is the distortion of an heavily overdriven opamp.
So, the key to prevent (or reduce significatly) opamps' own clipping without sucrificing the high gain. Let's move in my next though.
Let's say, I am building a 9V stompbox with some (3-4) low gain opamp stages (x5 - x10 each one), with clipping diodes/leds in each feedback to prevent opamp from clipping (rather than produce soft knee distortion), and maybe one-two voltage dividers across the signal. Also, some bass & treble roll of and some assymetry of the signal. Total gain is about 2500. This circuit could (I am just wondering) produce a polished and noble high gain distortion. Something like the transistorized Big Muff but with opamps. I draw a draft schematic to make my thoughts clear.

Is there something similar in the stompbox land?