I just used an MXR microamp clean boost and a Dunlop Wah with my Mk III for 20+ years but the past couple of years I've added a Fulltone OCD. I have this set as a bright crunchy mid level gain that sits between the low gain of R2 and a saturated eq'd Lead. My Mark III is a purple stripe so R2 is slightly warm. The OCD is nice and edgy.
I either use it into a clean R1 or to cream up R2. I don't need it with the lead channel.
The Fulltone OCD def. seems to work very well with the Mark iii. Recommended. It has both a bright & dark modes.
I was out playing last night and my boogie also had a Fulltone Fulldrive 3 to give more range of colour for a broad set of cover numbers. Cranked up a bit it is more tubescreamer like than the OCD and hits the mids nicely.
Finding the Fulltones has taken away my desire to look at a Mark 5 with more control of each channel as I can get all the clean, crunch and gain tones I want now.
Interesting. R2 on the MkIII is definitely wooly! It doesn't need more bass, although more edge would be helpful.
I sometimes use an MXR 10-band EQ as steroids for R2, although otherwise, I use only the tone straight from the amp. The Lead Channel comes from Mount Olympus and is always pure!! I sometimes use a distortion pedal through R1 for something totally different, such as a Marshall Shredmaster.