  We construct consistent theories of multiple interacting spin-2 fields in
arbitrary spacetime dimensions using a vielbein formulation. We show that these
theories have the additional primary constraints needed to eliminate potential
ghosts, to all orders in the fields, and to all orders beyond any decoupling
limit. We postulate that the number of spin-2 fields interacting at a single
vertex is limited by the number of spacetime dimensions. We then show that, for
the case of two spin-2 fields, the vielbein theory is equivalent to the
recently proposed theories of ghost-free massive gravity and bi-metric gravity.
The vielbein formulation greatly simplifies the proof that these theories have
an extra primary constraint which eliminates the Boulware-Deser ghost.
