  We construct a two parameter family of eleven-dimensional indecomposable
Cahen-Wallach spaces with irreducible, non-flat, non-restricted geometric
supersymmetry of fraction $\nu=\tfrac{3}{4}$. Its compactified moduli space can
be parametrized by a compact interval with two points corresponding to two
non-isometric, decomposable spaces. These singular spaces are associated to a
restricted $N=4$ geometric supersymmetry with $\nu=\tfrac{1}{2}$ in dimension
six and a non-restricted $N=2$ geometric supersymmetry with $\nu=\tfrac{3}{4}$
in dimension nine.
