Off course that is a great idea. Not sure if a pedal of that kind exists. You could used two SD-1's with different settings and toggle between them with a AB-box.
I was thinking of SD-2 but you will not get the same sound there.
When I read your post I was thinking about this pedal here.
https://reverb.com/item/33617635-aria-dt-10
It is not the sound of a SD-1 but it is a copy of a DS-1 and does exactly what you mentioned:
You can toggle between Stage 1 and Stage 2 to change your level of distortion without altering the basic sound. Really simple idea and not that many dist. pedals offer such a feature. Think about it, and this pedal is from the early 80s, really inventive and practical idea.
Just thinking, you could do it also by adding a EQ pedal. The GE-7 would do it as well since you can alter the level: Do not add-or cut anything of your EQ setting but alter the level, so you have created a boost to your sound. I know it is another extra pedal in your signal chain for such a simple feature, so it would be better to have something like that on just one pedal.
Cheers!