| MadSci Network: Physics |
I found the original paper by W.B. Kemplerer. It is in the Astronomical Journal, vol. 67, number 3 (April, 1962), on pages 162-7. The title is "Some Properties of Rosette Configurations of Gravitating Bodies in Homographic Equilibrium".
What Kemplerer shows in the paper is that an even number of bodies can orbit about their center of mass if certain properties are met. The arrangement of the bodies must have mirror symmetry about a radius from the common center to any of the bodies. The configurations will alternate heavier and lighter bodies. All of the heavier and all of the lighter bodies must have the same mass. It is possible for the "heavy" mass and the "light" mass to be the same. The ratio of the heavy mass to the light mass determines the orbital frequency and the ratio of the heavy mass orbital radii to the light mass orbital radii.
Kemplerer goes on to place certain restrictions on the available orbital radii ratios. The orbits of the bodies about the common center are ellipses of identical eccentricity. The bodies are allowed oscillations out of the orbital plane.
So to answer your question; yes, such things are possible, except that the number of bodies Kemplerer requires must be even. Since he does not place restrictions on the mass ratio, it may be that the light bodies could be quite small. He also notes that the arrangement is not stable under random perturbations, so an arrangement such as this would have to stay far away from other gravitating bodies.