  We consider the effective field theory of multiple interacting massive spin-2
fields. We focus on the case where the interactions are chosen so that the
cutoff is the highest possible, and highlight two distinct classes of theories.
In the first class, the mass eigenstates only interact through potential
operators that carry no derivatives in unitary gauge at leading order. In the
second class, a specific kinetic mixing between the mass eigenstates is
included non-linearly. Performing a decoupling and ADM analysis, we point out
the existence of a ghost present at a low scale for the first class of
interactions. For the second class of interactions where kinetic mixing is
included, we derive the full $\Lambda_3$ decoupling limit and confirm the
absence of any ghosts. Nevertheless both formulations can be used to
consistently describe an EFT of interacting massive spin-2 fields which, for a
suitable technically natural tuning of the EFT, have the same strong coupling
scale $\Lambda_3$. We identify the generic form of EFT corrections in each
case. By using Galileon Duality transformations for the specific case of two
massive spin-2 fields with suitable couplings, the decoupling limit theory is
shown to be a bi-Galileon.
