Two symmetric triblock polystyrene-butadiene-polystyrene (SBS) copolymers with different initial morphologies were grafted with varying amounts of isobutyl-substituted polyhedral oligomeric silsesquioxane (POSS) molecules. The POSS octamers, R'R7Si8O12, were designed to contain a single silane functional group, R', which was used to graft onto the dangling 1,2-butadienes in the polybutadiene block and seven identical organic groups, R = isobutyl (iBu). Morphology and phase transitions of these iBu-POSS-modified SBS were investigated using small-angle X-ray scattering and rheological methods. It was observed that when iBu-POSS was grafted to the butadiene segment, the long-range and local order of the morphology were preserved, and the d-spacing showed a small, systematic increase with increasing POSS content. These observations suggest that grafted iBu-POSS were well-distributed within the butadiene domains and did not interact with the styrene domains; effectively, grafting of iBu-POSS to butadiene did not affect the segregation between butadiene and styrene domains. However, addition of iBu-POSS reduces the overall polystyrene volume. Consequently, from a morphology standpoint, this modification effectively shifts the phase diagram to lower styrene content. This was supported with SAXS and transition temperatures measurements made from the different host morphologies.