The increasing integration of collaborative robots into industrial manufacturing processes necessitates continuous improvements in their mechanical properties. While collaborative robots are designed to enable flexible and safe human-robot interactions, their comparatively low structural stiffness poses a challenge for high-precision machining and heavy assembly tasks. Addressing this limitation is essential for enhancing performance by reducing deformation-related errors and improving overall efficiency in manufacturing processes. This paper proposes an approach for enhancing the stiffness of collaborative robots by means of situational coupling. Initially, an analysis is conducted to determine the kinematic limitations of coupled collaborative robots. Subsequently, the stiffness of coupled collaborative robots is modelled using the finite element method. Experimental stiffness measurements of a collaborative robot are utilized to validate this model. On basis of this model, it is demonstrated, that the approach of coupling has the potential to enhance the stiffness by up to 37.19 times in comparison with a solitary collaborative robot.