  We propose a new family of $\mathsf{U}(1)$ duality-invariant models for
nonlinear ${\cal N}=1$ supersymmetric electrodynamics coupled to supergravity.
It includes the Cribiori-Farakos-Tournoy-van Proeyen supergravity-matter theory
for spontaneously broken local supersymmetry with a novel Fayet-Iliopoulos term
without gauged $R$-symmetry. We present superconformal duality-invariant
models, as well as new $\mathsf{U}(1)$ duality-invariant models for
spontaneously broken local supersymmetry.
