Oh yes, an overdrive. I use an OD with almost all of my Mesa amps, up to and including the Dual Rectifier. Not necessarily to add distortion but rather to tighten up the sound (OD gain @0).
But to me, there's a difference between an OD and a "distortion pedal" - a significant one in the quantity if not quality of distortion. An OD (like any of the 1001 different TS808 variants) mostly boosts the amp's natural overdriven sound, and maybe adds a spice of its own, while a distortion pedal offers a distorted sound entirely on its own, like a Rat or Metal Zone pedal. And that's why I wondered why anybody would want to use a "distortion pedal" with a Mark III.
...that said, my current pedal board iactually also incorporates one genuine distortion pedal, a Wampler Triple Wreck, as recommended by fellow Boogie Board members. I'm using it to get faux-Recto sounds out of my Mark amplifiers when I'm too lazy to take my DR head with me to a band rehearsal.