This is dynamically unstable; Any miniscule imperfection ends up being magnified by the forces involved. The angular momentum of the system is conserved, but resonances build chaotically and are likely to eventually concentrate enough in a smaller body to throw it off past escape velocity.

Spaced-out resonant triplets of bodies in the same plane are often dynamically stable - an imperfect ratio is damped by various orbital forces until it approximates a perfect ratio.