We explore N=1supersymmetric extensions of algebras going beyond the Poincaré and AdS ones in three spacetime dimensions. Besides reproducing two known examples, we present new superalgebras, which all correspond to supersymmetric extensions with one fermionic charge Qαconcerning the so-called resonant algebras being characterized by the presence of an additional bosonic generator Za. We point out particular requirements that superalgebras have to satisfy to be successfully incorporated within valid supergravity actions. The presented algebraic and Lagrangian framework helps us better understand the relations between the various supergravity and supersymmetric Chern-Simons actions invariant under diverse resonant