Blending two simple polytopes together at vertices, at edges, or at other supplementary faces, produces another simple polytope. In pursuing the Hirsch conjectures, vertex-blends produced polytopes which have large diameter and few diametral paths. Here we define and explore blends at higher-dimensional faces. We identify specific blendings which would, given the proper inputs, produce counterexamples to the Hirsch conjecture. We also show that the Hirsch conjecture is sharp for dimension 7.