This paper addresses a class of deformation mechanisms involving the coordinated shear of multiple, parallel slip planes. Relevant phenomena include complex stacking faults, deformation twins, and dislocation nucleation ahead of cracks in metals. As part of the theory, we revisit the notion of a multi-plane slip potential, we develop a criterion for the emergence of microtwins, and we discern the conditions that favor microtwin versus dislocation nucleation. The model is constructed using concepts from the continuum-based Peierls-Nabarro framework for extended dislocation cores.