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The coupling with external mechanical systems such as oscillating masses working as tuned mass dampers, dynamic mass absorbers, elasto-plastic dampers, and rigid walls is an effective method to reduce the displacements and drifts of structures under external loads. An alternative method is provided by the coupling of the structure with an independent, auxiliary elasto-plastic system. This paper investigates the dynamic and seismic behaviour of a structure rigidly coupled with an auxiliary yielding mechanical system under harmonic and seismic ground excitation. A two-degree-of-freedom model is used to describe the dynamic and seismic behaviour of the main structure rigidly coupled to the yielding system, which is described by a one-degree-of-freedom model. The auxiliary system has an elasto-plastic constitutive behaviour that is modelled by a Bouc-Wen model. The equations of motion of the coupled system are obtained by a direct approach. The coupling with the yielding system is considered beneficial if the displacements of the coupled system reduce with respect to those of the stand-alone frame structure. An extensive parametric analysis is performed to point out the role of the mechanical parameters that describe the elasto-plastic constitutive behaviour of the auxiliary system. Results reveal that in large ranges of the parameters’ values, the coupling with the elasto-plastic system improves the performance of the frame structure.