This study explores the seismic interaction between a concrete moment-resisting frame and a rocking shear wall equipped with both longitudinal and perpendicular dampers. Unlike earlier works that placed dampers only along the wall’s length, this research introduces transverse dampers mounted perpendicularly using brackets. A parametric study examined how damper cross-sections affect displacement, drift, acceleration, and overturning safety. CFRP tendon post-tensioning forces were adjusted to ensure self-centering, with 160 KN per tendon found optimal. The structural response varied with damper cross-section. Unlike fixed-base systems where displacement consistently drops with larger dampers, rocking systems showed mixed trends. A 60×60 mm damper proved optimal for balancing displacement control and performance. Drift behavior followed conventional patterns, decreasing as damper size increased. A 246.7% drift reduction was observed with a 60×40 mm damper during the Kocaeli earthquake, but the 60×60 mm configuration with an MR/MO ratio of 0.93 was overall the most effective, combining stability and energy dissipation. Drift improvements became notable only after a specific damper size threshold, supported by time-history analysis from seven earthquakes. The study also found that the damper arrangement along the wall’s edges significantly affects the overturning safety factor, particularly in rocking systems.