  We investigate the space of consistent tree-level extensions of the maximal
supergravities in ten dimensions. We parametrize theory space by the first few
EFT coefficients and by the on-shell coupling of the lightest massive state,
and impose on these data the constraints that follow from $2 \to 2$
supergraviton scattering. While Type II string theory lives strictly inside the
allowed region, we uncover a novel extremal solution of the bootstrap problem,
which appears to contain a single linear Regge trajectory, with the same slope
as string theory. We repeat a similar analysis for supergluon scattering, where
we find instead a continuous family of extremal solutionswith a single Regge
trajectory of varying slope.
