Vertical extension of existing buildings is a sustainable and fascinating strategy for urban densification in contemporary cities, allowing for accommodating the growing demand for usable spaces with no land take. An innovative approach has been recently suggested by the authors to rise the building height while reducing the seismic demand on the existing structure: it consists of vertical addition equipped with seismic isolation at its base, realised on the roof of the existing structure, thus configuring as an Intermediate Isolation System (IIS) working as a nonconventional tuned mass damper. In this paper, the possibility of regularizing, as well as reducing, the dynamic response of the existing structure through an appropriate design of the isolation system is examined. For this purpose, an existing masonry building, with eccentricity between the stiffness and mass centroids, is selected and analysed as a case study. Several solutions for the isolation system, both in terms of period and distribution of isolators shear stiffnesses, are considered. Analysis results are discussed and design implications are suggested.