  We present two different families of eleven-dimensional manifolds that admit
non-restricted extensions of the isometry algebras to geometric superalgebras.
Both families admit points for which the superalgebra extends to a super Lie
algebra; on the one hand, a family of $N=1$, $\nu={}^3\!/\!_4$ supergravity
backgrounds and, on the other hand, a family of $N=1$, $\nu=1$ supergravity
background. Furthermore, both families admit a point that can be identified
with an $N=4$, $\nu={}^1\!/\!_2$ six-dimensional supergravity background.
