  We constrain theories of a massive spin-2 particle coupled to a massless
spin-2 particle by demanding the absence of a time advance in eikonal
scattering. This is an $S$-matrix consideration that leads to model-independent
constraints on the cubic vertices present in the theory. Of the possible cubic
vertices for the two spin-2 particles, the requirement of subluminality leaves
a particular linear combination of cubic vertices of the Einstein--Hilbert
type. Either the cubic vertices must appear in this combination or new physics
must enter at a scale parametrically the same as the mass of the massive spin-2
field. These conclusions imply that there is a one-parameter family of
ghost-free bimetric theories of gravity that are consistent with subluminal
scattering. When both particles couple to additional matter, subluminality
places additional constraints on the matter couplings. We additionally
reproduce these constraints by considering classical scattering off of a
shockwave background in the ghost-free bimetric theory.
