  Considering supergravity theory is a natural step in the development of
gravity models. This paper follows the ``algebraic`` path and constructs
possible extensions of the Poincar\'e and Anti-de-Sitter algebras, which
inherit their basic commutation structure. Previously achieved results of this
type are fragmentary and show only a limited fraction of possible algebraic
realizations. Our paper presents the newly obtained symmetry algebras,
evaluated within an efficient pattern-based computational method of generating
the so-called 'resonating' algebraic structures. These supersymmetric
extensions of algebras, going beyond the Poincar\'e and Anti-de Sitter ones,
contain additional bosonic generators $Z_{ab}$ (Lorentz-like), and $U_a$
(translational-like) added to the standard Lorentz generator $J_{ab}$ and
translation generator $P_{a}$. Our analysis includes all cases up to two
fermionic supercharges, $Q_{\alpha}$ and $Y_{\alpha}$. The delivered plethora
of superalgebras includes few past results and offers a vastness of new
examples. The list of the cases is complete and contains all superalgebras up
to two of Lorentz-like, translation-like, and supercharge-like generators
$(JP+Q)+(ZU+Y)=JPZU+QY$. In the latter class, among $667$ founded
superalgebras, the $264$ are suitable for direct supergravity construction. For
each of them, one can construct a unique supergravity model defined by the
Lagrangian. As an example, we consider one of the algebra configurations and
provide its Lagrangian realization.
