Don't some amps already, notoriously, do that? Mesa Boogie Triple Crest, Marshall Silver Jubilee, and some versions
of the JCM800 and JCM900 (among others) all have opamps and/or clipping diodes added into the preamp (aka a "pedal.")
Pretty sure the Jose Aredondo Mod of Marshall Superleads and Plexis also used some Zener diode clipping. Dave Friedman
used some of that same topology in the BE amps. Saturation switch ON = introduction of diode clipping into the circuit.
Someone else here probably knows more about that than I do.
JCM800 channel switching models 2210, 2205 and their combo derivatives all had clipping diodes, probably derived from reverse engineering Jose mods. They were not terribly popular back in the day, and I always struggled to love them as much as the straight Master Volume amps. Having said that, very rare that I ever used a 2203 or 2204 without goosing the front end with a drive pedal, so I'm not sure what i thought I was achieving by being so "purist".
I think the JCM800 2203 Kerry King signature model has a Tube Screamer effectively built into the preamp section. Bet they sound great.
Liam