This paper aims to determine whether additive manufacturing (AM) always simplifies the supply chain. The advent of AM as a final-parts production method can radically impact supply chains. Due to AM's inherent characteristics that suit customised production and complex geometries, utilization of this technology continues to expand into various industries (e.g. aviation, defence, automobile, medicine). Some of the crucial areas that AM can contribute to are cost reduction and simplification of organizations' supply chains. An objective examination of the entire supply chain rather than merely focusing on production cost is important when studying the impact of switch-over from conventional to additive manufacturing. Supply chain complexity is caused by the proliferation of products, processes, suppliers, and markets, resulting in additional costs and decreased company profit. Therefore, to clearly illustrate the benefits and shortcomings of a switch-over to AM, it is necessary to investigate this transition in depth. In this paper, we analysed supply chain complexity before and after the implementation of AM in three case companies from distinct industries by conducting interviews or utilizing publicly available information. Our findings underline the simplification of supply chain in one of the cases, after the switch to AM, while it resulted in slightly higher complexity in another case. In the third case, the impact of switching to AM on the supply chain complexity is dependent on several variables. We contribute to the literature by elucidating on the common belief that AM simplifies the supply chain. We found that the implementation of AM is not a silver bullet to reduce the complexity of every supply chain.