  Generalized membrane solutions of D=11 supergravity, for which the transverse
space is a toric hyper-K{\" a}hler manifold, are shown to have IIB duals
representing the intersection of parallel 3-branes with 5-branes whose
orientations are determined by their $Sl(2;\bZ)$ charge vectors. These IIB
solutions, which generically preserve 3/16 of the supersymmetry, can be further
mapped to solutions of D=11 supergravity representing the intersection of
parallel membranes with any number of fivebranes at arbitrary angles.
Alternatively, a subclass (corresponding to non-singular D=11 solutions) can be
mapped to solutions representing the intersection on a string of any number of
D-5-branes at arbitrary angles, again preserving 3/16 supersymmetry, as we
verify in a special case by a quaternionic extension of the analysis of
Berkooz, Douglas and Leigh. We also use similar methods to find new 1/8
supersymmetric solutions of orthogonally intersecting branes.
