  By means of a generalization of the S-expansion method we construct a
procedure to obtain expanded higher-order Lie algebras. It is shown that the
direct product between an Abelian semigroup S and a higher-order Lie algebra
($\mathcal{G},[,...,])$ is also a higher-order Lie algebra. From this
S-expanded Lie algebra are obtained resonant submultialgebras and reduced
multialgebras of a resonant submultialgebra.
