Fully understanding of multistate quantum systems could become formidable if not impossible as the system dimensionality increases. One ideal strategy to comprehend complex systems is to transform the system representation into a more structural one so that major characteristics, connections, and even underlying mechanisms can stand out from the huge unstructured information, e.g., the construction of spin eigenfunctions for a system of multiple spins through the diagonalization of the system Hamiltonian matrix. Here, instead of direct matrix diagonalization, the recently developed modular tensor diagram approach is applied to reorganize the state space structure of multispin systems, extending previous investigations on exciton pair states to exciton trimer states. This implementation demonstrates that the proposed approach not only provides a systematical way to transform the high dimensional multistate system into a well organized structure based on basic (exciton) modules but also paves the way to further analysis on potential applications. For example, the analysis on the state space of the exciton trimer system suggests a possible scheme to improve the laser performance via single fission involving multiexcitations and/or multiple fission steps.