We show how the S-matrix of an extended theory of gravity defined by its three-point amplitudes can be constructed by demanding factorisation. The resultant S-matrix has tree amplitudes obeying the same soft singularity theorems as Einstein gravity including the sub-sub-leading terms.
Dunbar, D. C., Godwin, J. H., Jehu, G. R., & Perkins, W. B. (2017). Diagrammar in an extended theory of gravity. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 771, 230–234. https://doi.org/10.1016/j.physletb.2017.05.052