  The $S$-expansion framework is analyzed in the context of a freedom in
closing the multiplication tables for the abelian semigroups. Including the
possibility of the zero element in the resonant decomposition and associating
the Lorentz generator with the semigroup identity element leads to the wide
class of the expanded Lie algebras introducing interesting modifications to the
gauge gravity theories. Among the results, we find all the Maxwell algebras of
type $\mathfrak{B}_m$, $\mathfrak{C}_m$, and recently introduced
$\mathfrak{D}_m$. The additional new examples complete resulting generalization
of the bosonic enlargements to an arbitrary number of the Lorentz-like and
translational-like generators. Some further prospects concerning enlarging the
algebras are discussed, along with providing all the necessary constituents for
constructing the gravity actions based on the obtained results.
