When I ask this I'm thinking of a system similar to ours, but the orbits are perfectly staggered and all planets involved have orbital periods such that when the planet (or small moon, whichever works better) is about to leave the umbra of one planet, another aligns in a way that the planet or moon is never exposed to direct light.
Thinking about this, perhaps a system would not be able to host enough planets in stable orbits to make this possible?