  Necessary and sufficient conditions are provided for a class of warped
product manifolds with non-vanishing flux to be supersymmetric solutions of 11D
supergravity. Many noncompact, but complete solutions can be obtained in this
manner, including the multi-membrane solution initially found by Duff and
Stelle. In a different direction, an explicit 5-parameter moduli space of
solutions to 11D supergravity is also constructed which can be viewed as
nonsupersymmetric deformations of the Duff-Stelle solution.
