This paper presents the results of an extensive (analytical and numerical) study carried out to investigate the effectiveness, for the mitigation of the seismic effects, of placing viscous dampers so that they connect the corresponding storeys of adjacent structures. These structures may be either two adjacent shear frame buildings or two portions of the same building (i.e. the structure and a lateral resisting element external or internal to the structure). This peculiar damper arrangement for inserting added viscous dampers in shear-type structures, if damper sizing is chosen appropriately, may be traced back to the indirect implementation of the so-called MPD (mass proportional damping) system which has been extensively studied in previous research works by the authors and has proved to be characterized by superior dissipative properties. A first analytical approach carried out with reference to a basic system composed of two adjacent SDOF systems linked by a single damper is developed in order to understand the physical properties which govern the problem in question. Then, a wide series of numerical simulations is carried out with reference to the following two cases: (case 1) insertion of dampers between two adjacent structures characterized by different dynamic properties and (case 2) insertion of dampers between a frame structure and a very stiff lateral resisting element. The results show that this peculiar damper placement is capable of providing damping effects upon both the structures which are larger than those which could be provided by typical interstorey damper placements as applied to each distinct structure. In detail, for case 1, the parametric study here presented provides indications regarding how different the dynamic properties of the two linked structures must be in order to achieve a good damping efficiency of the system thus obtained. For case 2, results indicate that, for common building structures, insertion of dampers between a frame structure and the lateral resisting core leads, in general, to a good damping efficiency. These results can open the ground for new paths for a new and efficient conceptual design of structures to be built in seismic areas.