Integrating a tuned liquid multi-column damping (TLMCD) into a floating offshore wind turbine (FOWT) is challenging. The synergy between the TLMCD, the turbine controller, and substructure dynamics affects the FOWT's performance and cost. A control co-design optimization framework is developed to optimize the substructure, the TLMCD, and the blade pitch controller simultaneously. The results show that the optimization can significantly enhance FOWT system performance.