  Self-interacting massive particles with spin $\geq 1$ unavoidably violate
unitarity; the question is at what scale. For spin-$1$ the strong coupling
scale (at which perturbative unitarity is lost) cannot be raised by any finite
tuning of the interactions, while for spin-$2$ there exists a special tuning of
the Wilson coefficients which can raise this scale (and enjoys numerous special
properties such as ghost-freedom). Here, we fill in the missing piece by
describing how the self-interactions of a massive spin-$3/2$ field, or "massive
gravitino", become strongly coupled at high energies. We show that while
several different structures appear in the leading order potential, the strong
coupling scale cannot be raised (in the absence of additional fields). At the
level of the off-shell Lagrangian, it is always the non-linear symmetries of
the longitudinal Stuckelberg mode that dictate the strong coupling, and we show
that in general it is only possible to parametrically raise the strong coupling
scale if Wess-Zumino structures exist. We complement this off-shell approach
with a first analysis of positivity bounds for a massive spin-$3/2$ particle,
showing that any potential self-interaction which contributes to an on-shell
2-to-2 elastic process at tree level must vanish if this low-energy theory is
to have a standard UV completion. We identify the mixing between the
longitudinal mode and the transverse modes as the main obstacle to positivity,
and clarify how the non-Abelian nature of non-linear (dRGT) massive gravity
allows it to satisfy positivity where all known spin $\geq 3/2$ Abelian
theories fail. Our results imply that a massive gravitino cannot appear alone
in a controlled EFT---it must be accompanied by other particles, e.g.~as part
of a supermultiplet. Together with the spin-$1$ and spin-$2$ cases, we suggest
features which will persist in even higher spin massive theories.
