We propose a method for unsupervised many-to-many object matching from multiple networks, which is the task of finding correspondences between groups of nodes in different networks. For example, the proposed method can discover shared word groups from multi-lingual document-word networks without cross-language alignment information. We assume that multiple networks share groups, and each group has its own interaction pattern with other groups. Using infinite relational models with this assumption, objects in different networks are clustered into common groups depending on their interaction patterns, discovering a matching. The effectiveness of the proposed method is experimentally demonstrated by using synthetic and real relational data sets, which include applications to cross-domain recommendation without shared user/item identifiers and multi-lingual word clustering.