$$ \mathcal{N} $$ = 2 extended MacDowell-Mansouri supergravity

We construct a gauge theory based in the supergroup $G=SU(2,2|2)$ that generalizes MacDowell-Mansouri supergravity. This is done introducing an extended notion of Hodge operator form outer automorphism $su(2,2|2)$-valued 2-form tensors. The model closely resembles Yang-Mills -- including action principle, equations motion and transformations which avoids use otherwise complicated component formalism. enjoys $H=SO(3,1)\times \mathbb{R} \times U(1)\times SU(2)$ off-shell symmetry whilst broken symmetries $G/H$, translation-type supersymmetry, can be recovered on surface integrability conditions motion, for it suffices Rarita-Schwinger equation torsion-like constraints to hold. Using \textit{matter ansatz} projecting $1 \otimes 1/2$ reducible representation into spin-$1/2$ irreducible sector we obtain (chiral) fermion models with gravity interactions.