Improving　the　seismic　response　of　new　and　existing　structures　is　a　fundamental　topic　in　civil　engineering.　Often,　in　structural　mechanics　this　issue　is　addressed　through　low-dimensional　mechanical　models　capable　of　capturing　the　primary　dynamics　of　the　structure.　In　contrast　to　most　studies　in　the　scientific　literature　that　use　two-dimensional　models　to　describe　structural　behavior,　this　paper　employs　a　low-dimensional,　three-dimensional　(3D)　mechanical　model　to　capture　the　seismic　response　of　a　structure,　also　accounting　for　its　torsional　effects.　This　low-dimensional　model　is　used　to　investigate　two　different　methods　for　improving　seismic　response.　One　approach　involves　inerter　devices　directly　connected　to　the　structure,　while　the　other　is　based　on　connecting　the　structure　to　external　auxiliary　structures,　equipped　in　turn　with　inerters.　Therefore,　in　this　case,　the　inerter　devices　are　connected　directly　to　the　external　structures.　The　responses　of　the　original　stand-alone　frame　structure　and　those　with　the　two　proposed　methods　are　compared　to　assess　the　effectiveness　of　each　approach.　Three　different　earthquake　records　are　used　as　base　excitation.　The　results　are　presented　in　performance　curves　and　maps,　showing　the　response　in　terms　of　displacements　of　key　points　of　the　structure　as　various　system　parameters　are　varied.　The　results　reveal　the　good　performance　of　both　methods　over　a　wide　range　of　parameters,　with　particularly　favorable　results　for　the　approach　using　external　structures　equipped　with　inerter　devices.　Copyright　©　2025　Di　Egidio　and　Contento.