Looking into it, couldn't a planet orbit one of the two stable Lagrange points between the two groups, L4 and L5? That wouldn't be "inside" the orbit though :(
Yeah, I would think that the quasi stable orbits would be L4, L5 or orbiting around any of the pairs. If you have a symmetric situation isn't the middle point exactly L1? That would be unstable.
Edit: From Wikipedia:
>The triangular points (L4 and L5) are stable equilibria, provided that the ratio of M1/M2 is greater than 24.96.
So with a symmetric situation, where M1/M2=1 they wouldn't be stable either.
There could be stable point's in the middle, I don't know about that. Most certainly it can't be described by this approximation.