  We consider the deconstruction/reconstruction of extensions in varieties of
algebras which are modules expanded by multilinear operators. The
parametrization of extensions determined by abelian ideals with unary actions
agrees with the previous development of extensions realizing affine datum in
arbitrary varieties of universal algebras. We establish a Well's type theorem
which, for a fixed affine ideal, characterizes those ideal-preserving
derivations of a group-trivial extension as a Lie algebra extension of the
compatible pairs of derivations of the datum algebras associated to the ideal
by the cohomological derivations of the datum. For these varieties, we
establish a low-dimensional Hochschild-Serre exact sequence associated to an
arbitrary extension equipped with an additional affine action.
