There are a *lot* of dual function pedals out there now. Even within dirt offerings, you can choose from countless permutations of boost/overdrive/distortion.
For distortion/boost, I currently use the Bogner La Grange for Marshall tones. I like the boost because it is very clean and controllable.
I have 2 overdrive/boost pedals, the EHX Tortion and Carl Martin DC Drive. They are both good, but I don't use them because I have other single-purpose pedals I prefer for overdrive.
The EXH Germanium 4 Big Muff Pi is nominally a distortion/overdrive, though it seems to be strongly fuzz-flavored, given the "Big Muff" part. The clips of it sound super interesting, as it produces a very wide range of sounds.
The original Carl Martin Plexitone could be a competitor to the Fly Rig. It has 3 functions. It has 2 channels of Marshall-esque dirt and a boost. The second channel is high gain, like really high gain.
The Carl Martin AC Tone Dual Overdrive works the same way, though it has much less gain than the Plexitone.