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Matter would have to accrete equally at six equally spaced points, which as others have pointed out has a problem with getting started in the first place.
The other problem is that a protoplanetary disk is not uniform, so even if by some miracle, six things of equal mass started out at six equally spaced points along one orbit, one of them would almost certainly accrete more mass than the others.
That would throw the Lagrange points out of alignment, if not also slow the orbit of that body, and I imagine that would quickly lead to runaway loss of equilibrium.
You are free to imagine them going on to happy existences in separate orbits, perhaps with a sweet system of resonances around the star, but something tells me that's unlikely.
On the other hand, there's a neat fiction story in there somewhere if you want to apply it to our own inner planets. Mercury, Venus, proto-Earth, Theia, Mars and the asteroid belt happen to number exactly six.