The implementation of dissipative dampers between adjacent buildings can effectively mitigate structural vibration responses, with inerter dampers offering distinct advantages for controlling coupled structures. However, the performance of different types of inerter dampers in adjacent buildings requires further investigation. This study aims to determine the optimal parameters of various control devices for multi-story adjacent structures. A global optimization solver is employed, with displacement and acceleration of the flexible structure as the primary control objectives, while constraining the response of the rigid structure. Three damper types, namely, viscoelastic dampers (VED), tuned inerter dampers (TID), and tuned viscous mass dampers (TVMD), are individually applied to adjacent structures to evaluate the influence of structural period ratio and damper placement on seismic response. The control efficacy of VED, TID, and TVMD is systematically compared, and a novel hybrid control scheme combining TID and TVMD is proposed. Time-history analysis confirms the effectiveness of the optimized design. Numerical results indicate that inerter dampers (TID and TVMD) significantly reduce the seismic response of adjacent structures while requiring considerably smaller damping parameters than VED. Although the hybrid TID-TVMD system demands higher parametric requirements than single-damper configurations, it achieves superior balance in controlling both displacement and acceleration of the flexible structure.