string amplitudes would appear truly miraculous. This prompts the question: is string theory the unique framework for a higher spin extension of gravity?  We investigate this question by bootstrap methods, focussing on maximal 10D supergravity. 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 causality and positivity constraints. 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.  We repeat a similar analysis for supergluon scattering.