Additive manufacturing (AM), also known as 3D printing, offers many advantages and, particularly in the medical field, it has stood out for its potential for the manufacture of patient-specific implantable devices. Thus, the unique properties of 3D-printed biocompatible polymers such as Polylactic Acid (PLA) and Polyetheretherketone (PEEK) have made these materials the focus of recent research where new post-processing and joining techniques need to be investigated. This study investigates the weldability of PLA and PEEK 3D-printed plates through stationary shoulder friction stir welding (SS-FSW) with assisted heating. An SS-FSW apparatus was developed to address the challenges of rotating shoulder FSW of thermoplastics, with assisted heating either through the shoulder or through the backing plate, thus minimizing material removal defects in the welds. Successful welds revealed that SS-FSW improves surface quality in both PLA and PEEK welds compared to rotating shoulder tools. Process parameters for PLA welds are investigated using the Taguchi method, emphasizing the importance of lower travel speeds to achieve higher joint efficiencies. In PEEK welds, the heated backing plate proved effective in increasing process heat input and reducing cooldown rates which were associated with higher crystallinity PEEK. Despite these findings, further research is needed to improve the weld strength of SS-FSW with these materials considering aspects like tool design, process stability, and 3D printing parameters. This investigation emphasizes the potential of SS-FSW in the assembly of thermoplastic materials, offering insights into the weldability of additively manufactured biocompatible polymers like PLA and PEEK.