With the global view and high-cadence observations from Solar Dynamics Observatory/Atmospheric Imaging Assembly and Solar TErrestrial RElations Observatory, many spatially separated solar eruptive events appear to be coupled. However, the mechanisms for "sympathetic" events are still largely unknown. In this study, we investigate the impact of an erupting flux rope on surrounding solar structures through large-scale magnetic coupling. We build a realistic environment of the solar corona on 2011 February 15 using a global magnetohydrodynamics model and initiate coronal mass ejections (CMEs) in active region 11158 by inserting Gibson-Low analytical flux ropes. We show that a CME's impact on the surrounding structures depends not only on the magnetic strength of these structures and their distance to the source region, but also on the interaction between the CME and the large-scale magnetic field. Within the CME expansion domain where the flux rope field directly interacts with the solar structures, expansion-induced reconnection often modifies the overlying field, thereby increasing the decay index. This effect may provide a primary coupling mechanism underlying the sympathetic eruptions. The magnitude of the impact is found to depend on the orientation of the erupting flux rope, with the largest impacts occurring when the flux rope is favorably oriented for reconnecting with the surrounding regions. Outside the CME expansion domain, the influence of the CME is mainly through field line compression or post-eruption relaxation. Based on our numerical experiments, we discuss a way to quantify the eruption impact, which could be useful for forecasting purposes.