Recent experiments by Ryu, Hermel, and co-workers have demonstrated a correlation between the presence of bridging A-blocks and practical toughness in themoplastic ABABA pentablock copolymers. Building on this observation, we develop a computational tool for evaluating average bridging fractions of internal blocks in complex block copolymers and apply the tool to the optimization of bridging fractions in mesophase structures computed with self-consistent-field theory. We identify optimal molecular designs for ABABA pentablock copolymers that could provide the useful combination of high modulus and high toughness. Further applications of the approach to property screening in complex mesophases formed by ABC and ABCA block copolymers are discussed.