  The Abelian semigroup expansion is a powerful and simple method to derive new
Lie algebras from a given one. Recently it was shown that the $S$-expansion of
$\mathfrak{so}\left( 3,2\right) $ leads us to the Maxwell algebra
$\mathcal{M}$. In this paper we extend this result to superalgebras, by proving
that different choices of abelian semigroups $S$ lead to interesting $D=4$
Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra
$s\mathcal{M}$ and the $N$-extended Maxwell superalgebra $s\mathcal{M}^{\left(
N\right) }$ recently found by the Maurer Cartan expansion procedure, are
derived alternatively as an $S$-expansion of $\mathfrak{osp}\left( 4|N\right)
$. Moreover we show that new minimal Maxwell superalgebras type
$s\mathcal{M}_{m+2}$ and their $N$-extended generalization can be obtained
using the $S$-expansion procedure.
