  We explicitly construct every kinematically allowed three particle
graviton-graviton-$P$ and photon-photon-$P$ S-matrix in every dimension and for
every choice of the little group representation of the massive particle $P$. We
also explicitly construct the spacetime Lagrangian that generates each of these
couplings. In the case of gravitons we demonstrate that this Lagrangian always
involves (derivatives of) two factors of the Riemann tensor, and so is always
of fourth or higher order in derivatives. This result verifies one of the
assumptions made in the recent preprint \cite{Chowdhury:2019kaq} while
attempting to establish the rigidity of the Einstein tree level S-matrix within
the space of local classical theories coupled to a collection of particles of
bounded spin.
