Event extraction has a trend in identifying event triggers and arguments in a unified framework, which has the advantage of avoiding the cascading failure in pipeline methods. The main problem is that joint models usually assume a one-to-one relationship between event triggers and arguments. It leads to the argument multiplexing problem, in which an argument mention can serve different roles in an event or shared by different events. To address this problem, we propose a multigraph-based event extraction framework. It allows parallel edges between any nodes, which is effective to represent semantic structures of an event. The framework enables the neural network to map a sentence(s) into a structurized semantic representation, which encodes multi-overlapped events. After evaluated on four public datasets, our method achieves the state-of-the-art performance, outperforming all compared models. Analytical experiments show that the multigraph representation is effective to address the argument multiplexing problem and helpful to advance the discriminability of the neural network for event extraction.