Seeking a more flexible and efficient production, additive manufacturing (AM) has emerged as a major player in the industrial field, streamlining the fabrication of custom tangible assets by directly 3D printing them. However, production still takes too long due to printing, but also due to the product design stage, in which the customer works together with an expert to create a 3D model of the targeted product by means of computer-aided design (CAD) software. Skipping intermediate agents and making customers responsible for the design process will reduce waiting times and speed up the manufacturing process. This work is conceived as a first step towards that optimized AM model, being aimed at bringing CAD tools closer to clients through an enhanced user experience, and consequently at simplifying pre-manufacturing design tasks. Specifically, as an alternative to the traditional user interface operated with the keyboard and mouse duo, standard in CAD and AM, the paper presents a comprehensive multi-touch interaction system conceived as a customer-centric human-machine interface. To depict the proposed solutions, we adopt furniture manufacturing as a case study and, supported by a CAD-like software prototype for 3D modeling of custom cabinets introduced in a previous work of the authors, we assess our approach’s validity in terms of usability by conducting in-lab and remote user studies. The comparison between the designed multi-touch interaction and its desktop alternative yields promising results, showing improved performance and higher satisfaction of the end-user for the touch-based approach, that lay the groundwork for a smarter factory vision based on remotely-operated AM.