  We explore $\mathcal{N}=1$ supersymmetric extensions of algebras going beyond
the Poincar\'e 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 $Q_{\alpha}$ concerning the
so-called resonant algebras being characterized by the presence of an
additional bosonic generator $Z_{a}$, besides the Lorentz $J_{a}$ and
translation $P_{a}$ generators. Obtained eight supersymmetric $JPZ+Q$ schemes
result directly from obeying super-Jacobi identities. We point out particular
requirements that superalgebras have to satisfy to be successfully incorporated
within valid supergravity actions. The presented algebraic and Lagrangian
framework organizes and helps us better understand relations between the
various supergravity and supersymmetric Chern-Simons actions invariant under
diverse resonant superalgebras.
