  We use generalized elastic positivity bounds to constrain the parameter space
of multi-field spin-2 effective field theories. These generalized bounds
involve inelastic scattering amplitudes between particles with different
masses, which contain kinematic singularities even in the $t=0$ limit. We apply
these bounds to the pseudo-linear spin-2 theory, the cycle spin-2 theory and
the line spin-2 theory respectively. For the pseudo-linear theory, we exclude
the remaining operators that are unconstrained by the usual elastic positivity
bounds, thus excluding all the leading (or highest cutoff) interacting
operators in the theory. For the cycle and line theory, our approach also
provides new bounds on the Wilson coefficients previously unconstrained,
bounding the parameter space in both theories to be a finite region ({\it
i.e.}, every Wilson coefficient being constrained from both sides). To help
visualize these finite regions, we sample various cross sections of them and
estimate the total volumes.
