Additive manufacturing (AM) has had a significant impact on manufacturing processes in many industries, which is expected to increase much further in the coming years. AM is, however, not easy to implement, as this involves several knowledge-related challenges, particularly for small and medium-sized enterprises (SMEs). To add to the understanding of this phenomenon, we develop a theoretical model that describes the use of external networks for overcoming such challenges in part by acquiring AM knowledge to increase internal AM maturity. We test our model of direct and mediated network effects on AM-related competitive advantages through a survey of Danish manufacturing SMEs. The results show that increased AM maturity explains around 40 percent of the relationship between knowledge acquisition from networks and AM-related competitive advantages. Results also show that building internal AM maturity was especially driven by networking with AM developers, AM suppliers, and AM organizations, while networking with AM consultants and other AM users promoted competitive advantages through other mechanisms. This suggests two overall strategies for achieving competitive advantages from AM: (1) using networks to build AM maturity, and (2) using external AM resources to compensate for low internal AM maturity.