Thermoplastic elastomers (TPEs) based on polystyrene (PS) are commonplace in society. The elastomeric properties of these materials are often sacrificed to increase mechanical properties such as stiffness, strength, and toughness. We sought to produce stiff, strong, and tough TPEs that retain their elastomeric properties by shifting the lamellar phase boundary toward higher PS content. By precisely controlling the molecular weight distribution (MWD) shape of one PS block in polystyrene-block-polyisoprene-block-polystyrene (SIS), we produced elastomeric continuous phase TPEs at atypically high PS volume fractions, shifting the lamellar phase boundary from 0.33 in triblocks with a narrow MWD PS block to similar to 0.39 in triblocks with a broadened MWD PS block. Furthermore, we observed hexagonal/lamellar phase coexistence at a PS volume fraction of 0.39 when the MWD shape of the first PS block was asymmetric. These materials exhibit enhanced mechanical properties consistent with high volume fractions of PS and elastomeric properties consistent with continuous morphologies.