Modular methodologies for the development and verification of concurrent/distributed systems are increasingly relevant nowadays. We investigate the simultaneous composition of multiple systems in a multiparty-session-type setting, working on suitable notions of interfacing policy and multicompatibility. The resulting method is conservative (it alters as less as possible the single systems), flexible (any system can be looked at as potentially open) and safe (relevant communication properties, e.g. lock-freedom, are preserved by composition). We obtain safety, by proving preservation of typability, and give a sound and complete type inference algorithm.