The morphologies formed by block copolymers with a double-graft, pi or (S,I)I＇(S,I) architecture were investigated using transmission electron microscopy (TEM) and small angle neutron scattering (SANS). Here S and I represent blocks of polystyrene and polyisoprene, respectively. These materials were synthesized using anionic polymerization and chlorosilane linking, and they were characterized using size exclusion chromatography, membrane osmometry, and low-angle laser light scattering. This characterization work confirmed the desired molecular architectures and narrow molecular weight distributions. The results of morphological characterization indicate that one can understand complex grafting architectures by decomposing them into fundamental building blocks, which are taken as the component single-graft structures out of which the larger structure is constructed. We propose rules for dividing structures into these components, which we call constituting block copolymers. For the a double-graft architecture, the constituting block copolymer is an asymmetric single-graft block copolymer. The morphological behaviour of the more complex double-graft architecture is approximately equivalent to that of the constituting single-graft block copolymer. Through the use of the constituting block copolymers we map the experimentally determined morphological behaviour of eight materials with a architecture onto the morphology diagram calculated by Milner for miktoarm stars. As in our previous study of asymmetric single-graft block copolymers, the asymmetry of the graft location along the backbone requires a generalization of the molecular asymmetry parameter, epsilon, used in the calculated morphology diagram.