Special Moment Frames (SMFs) require prequalified connections based on the strong column–weak beam principle. However, AISC 358 does not provide guidelines for continuity plates in hollow structural section (HSS) columns. To address installation challenges, vertical stiffeners have been proposed as an alternative, following a certain fabrication procedure. This study evaluates the influence of continuity plates and vertical stiffeners on SMF connections using finite element analysis (FEA) in Abaqus. A horizontal displacement of 5% of the column length was applied to assess structural performance, with variations in continuity plate thickness and width, and vertical stiffener thickness and length. Results indicate that local deformations occurred in the panel zone despite meeting the strong column–weak beam criterion, emphasizing the critical role of continuity plates. Plastic hinge formation in beams confirmed the adequacy of AISC 358 for determining continuity plate thickness, though modifications are recommended for vertical stiffeners. Shorter, thicker stiffeners proved more effective than longer, thinner ones.