  The non-standard intersection of two 5-branes and a string can give rise to
AdS_3\times S^3\times S^3\times S^1. We consider the Penrose limit of this
geometry and study the supersymmetry of the resulting pp-wave solution. There
is a one-parameter family of Penrose limits associated with the orthogonal
rotation of the two foliating circles within the two 3-spheres. Supernumerary
Killing spinors arise only when the rotation angle is 45 degrees, for which
case we obtain the corresponding light-cone string action that has
linearly-realised supersymmetry. We also obtain Penrose limits of other
non-standard intersections that give rise to the product of AdS_3 or AdS_2 and
two spheres. The resulting pp-waves are supported by multiple constant field
strengths.
