  We derive an on-shell diagram recursion for tree-level scattering amplitudes
in $\mathcal{N}=7$ supergravity. The diagrams are evaluated in terms of
Grassmannian integrals and momentum twistors, generalising previous results of
Hodges in momentum twistor space to non-MHV amplitudes. In particular, we
recast five and six-point NMHV amplitudes in terms of $\mathcal{N}=7$
R-invariants analogous to those of $\mathcal{N}=4$ super-Yang-Mills, which
makes cancellation of spurious poles more transparent. Above 5-points, this
requires defining momentum twistors with respect to different orderings of the
external momenta.
