Solving constrained multimodal multi-objective optimization problems (CMMOPs) is a complex task that requires a delicate balance between the feasibility of constraints, the convergence of objective space, and the diversity of decision space and objective space. Given the scarcity of effective algorithms for CMMOPs, this paper designs and implements a constrained multimodal multi-objective optimization algorithm PPS-CMMO based on an improved PPS framework. The algorithm applies the improved PPS framework to the solution of CMMOPs for the first time, and uses a parameter-free Affinity Propagation (AP) clustering method to divide the population into multiple sub-populations. The algorithm dynamically adjusts the update strategy of the sub-population according to the reference points at different evolution stages. This paper compares PPS-CMMO with eight algorithms on the CMMOPs benchmark problem set, which shows that the algorithm can successfully find multiple equivalent CPSs when processing CMMOPs. At the same time, our experiments also demonstrate that the algorithm is promising to solve MMOPs.