<p>Many real-world problems can be considered as multimodal multi-objective optimization problems (MMOPs), which feature multiple equivalent Pareto sets (PSs) corresponding to the same Pareto front (PF). Balancing the convergence and diversity in both the decision space and objective space while considering global and local PSs poses a significant challenge, with limited studies addressing it. In this paper, we propose a novel multimodal multi-objective state transition algorithm (MMOSTA) designed to locate multiple well-distributed and well-converged equivalent PSs and PFs simultaneously. The proposed MMOSTA encompasses several key steps. Firstly, local evaluation indicators such as the computation of local convergence indicator and local density evaluation indicator are established to preserve solutions from various PSs while achieving rapid convergence. Secondly, four state transition operators are utilized to generate new candidate solutions based on development progress due to their exploitation capabilities. Furthermore, a selection strategy based on local evaluation indicators that incorporates local PSs into the population is employed to enhance the overall performance of the population. Finally, the effectiveness of the proposed MMOSTA is verified through numerous case studies.</p>