The　toggle-brace-damper　system　(TBDS)　is　an　effective　displacement　amplification　damper　occupying　a　large　building　space.　The　small　deformation　solution,　which　is　widely　used,　cannot　describe　the　feature　that　the　displacement　amplification　capacity　varies　with　the　lateral　displacement　of　the　TBDS.　This　is　not　conducive　to　investigate　the　performance　of　the　TBDS　comprehensively.　Therefore,　the　geometric　design　and　optimization　of　the　TBDS　are　lack　of　a　theoretical　basis.　A　generalized　toggle-brace-damper　system　(GTBDS),　a　generalized　form　of　TBDS,　is　proposed.　It　has　a　flexible　layout　and　optimizes　the　space　available.　We　also　introduce　an　amplification　factor　of　displacement　increment　(AFDI)　that　can　accurately　describe　the　performance　of　the　GTBDS.　The　amplification　capacity　and　the　geometric　sensitivity　are　two　aspects　of　the　performance.　The　influence　of　geometric　parameters　on　the　performance　of　the　GTBDS　is　clarified　based　on　the　AFDI.　Some　regulations　are　also　proposed　to　compare　the　performance　of　GTBDSs　with　different　geometric　constructions.　Two　geometric　parameter　optimization　methods　of　the　GTBDS　are　proposed　to　balance　its　amplification　capacity,　operation　safety　and　geometric　sensitivity.　The　relationship　between　the　displacement　amplification　capacity　and　the　energy　dissipation　capacity　of　the　GTBDS　is　examined.　The　existing　modal　energy　dissipation　method　(MEDM)　is　extended　to　calculate　the　additional　damping　ratio　(ADR)　provided　by　the　GTBDS.　Combining　the　calculation　method　of　ADR　and　the　geometric　optimization　methods　of　GTBDS,　a　multiperformance　objectives　design　method　of　the　GTBDS　is　proposed.　The　case　analysis　verifies　the　effectiveness　and　the　feasibility　of　the　design　method.