Of course, the main reason we have little data on this is that we couldn't see most of them if they were there, and the fact that multiple star systems are less frequent than binary and single star systems reduces the number of opportunities we have near us where there is some hope of seeing one.
I don't see any inherent reason you shouldn't be able to have planets in a system with three or more stars. For example, suppose you had one very big star (a red giant maybe) and perhaps three smallish dwarf stars. They could easily have stable orbits with respect to each other similar to the Sun-Jupiter-Saturn-Neptune system. Basically, it could have orbits similar to our own system with every object in it put on steroids. Each star would have "moons" and voila, you have a nice happy family of planets, although instead easier to observe gas giants, they would probably be mostly the rocky small kind that are hard to see with telescopes.
From the point of view of a planet circling one of the dwarf stars, you would have a dim "sun" and then three relatively "moons" (which might be pretty dim at appropriate distances) that were almost always bright instead of going through phases.