  In this work we present an alternative method to construct diverse
non-relativistic Chern-Simons supergravity theories in three spacetime
dimensions. To this end, we apply the Lie algebra expansion method based on
semigroups to a supersymmetric extension of the Nappi-Witten algebra. Two
different families of non-relativistic superalgebras are obtained,
corresponding to generalizations of the extended Bargmann superalgebra and
extended Newton-Hooke superalgebra, respectively. The expansion method
considered here allows to obtain known and new non-relativistic supergravity
models in a systematic way. In particular, it immediately provides an invariant
tensor for the expanded superalgebra, which is essential to construct the
corresponding Chern-Simons supergravity action. We show that the extended
Bargmann supergravity and its Maxwellian generalization appear as particular
subcases of a generalized extended Bargmann supergravity theory. In addition,
we demonstrate that the generalized extended Bargmann and generalized extended
Newton-Hooke supergravity families are related through a contraction process.
