Polymers play a crucial role in various applications, and the synthesis of copolymers, which combine multiple monomers, offers unique material properties. In this study, we focus on the terpolymerization of styrene, myrcene, and dibutyl itaconate, aiming to discover Styrene-Myrcene-Dibutyl Itaconate terpolymers with high glass transition temperatures (Tg). High Tg enables their utilization in high-temperature environments. Notably, while copolymerization systems involving two monomers have been extensively investigated, the terpolymerization of styrene, myrcene, and dibutyl itaconate remains unexplored. Our goal is to synthesize a "green" terpolymer with minimal styrene incorporation, maximizing the use of renewable monomers. To achieve this, we adopt a multi-objective Bayesian optimization approach to simultaneously optimize for the Tg and styrene incorporation Our results demonstrate a Tg range of -53.36°C to 45.94°C and styrene incorporation ranging from 0.9 mol% to 84.7 mol%. This study contributes to the field of polymer science, showcasing the potential of Bayesian optimization in accelerating the discovery of novel terpolymer materials with desired properties.