“We are not like the social insects. They have only the one way of doing things and they will do it forever, coded for that way. We are coded differently, not just for binary choices, go or no-go. We can go four ways at once, depending on how the air feels: go, no-go, but also maybe, plus what the hell let’s give it a try.” -Lewis Thomas
One of the most important characteristics of a planet, at least according to the IAU definition, is that it clear its orbit of all other bodies. But if we allowed for a special caveat — the possibility of two similarly-sized objects sharing the same orbit — could we have a stable configuration where that occurred?
Surprisingly, not only is the answer yes, but there are three ways to do it: to have one at the L4/L5 Lagrange point of the other, to have a close-orbiting binary planet, or to have orbit-swapping worlds, where they periodically change spots with one another. Unbelievably, our Solar System has a history of all three!