  Key to the simplicity of supergravity $\alpha$-attractor models of inflation
are Volkov-Akulov fermions, often in the form of nilpotent superfields. Here we
explore the possibility of using the double-copy to construct theories of
Dirac-Born-Infeld-Volkov-Akulov (DBIVA) coupled to supergravity. A color-dual
bootstrap admits scattering amplitudes involving pions and vectors through
five-point tree-level order by order in mass-dimension, but requires the
introduction of a $\text{Tr}(F^3)$ operator. Gauge theories with this operator
were recently found to require a tower of higher-derivative operators to be
compatible with color-kinematics duality. Adjoint-type double-copy construction
at its most conservative seems to require the UV completion of DBIVA + pure
Poincar\'{e} supergravity scattering amplitudes to a family of theories
involving DBIVA-like particles coupled to Weyl-Einstein supergravity. We also
point out an alternative solution to color-dual gauged pions that allows
adjoint double-copy without a tower of higher derivative corrections but at the
cost of exchange symmetry between scalars.
