Large-scale　structures,　e.g.,　long-span　bridge　structures,　are　prone　to　induce　multi-modal　vibrations　due　to　their　densely　spaced　low　modal　frequencies.　Due　to　the　limited　frequency　bandwidth　of　linear　dynamic　absorbers,　they　are　incapable　of　effectively　mitigating　vibrations　across　multiple　modes.　To　this　end,　the　bistable　nonlinear　energy　sink　inerter　(BNESI)　is　used　to　mitigate　the　multimodal　vortex-induced　vibration　(VIV)　of　the　beam　structure.　The　highly　nonlinear　equilibrium　differential　equations　of　the　beam-BNESI　system　are　numerically　solved,　and　the　simulated　annealing　(SA)　algorithm　is　employed　to　determine　the　optimal　VIV　reduction　ratio　and　BNESI　parameters.　In　comparison　to　the　cubic-type　nonlinear　energy　sink　inerter　(CNESI),　BNESI　is　found　to　possess　more　stable　equilibrium　positions,　smaller　stiffness　coefficients,　and　higher　VIV　mitigation　efficiency.　The　selection　of　design　modes　has　been　found　to　influence　the　efficiency　of　multimodal　VIV　mitigation,　with　the　use　of　the　intermediate　modal　order　as　the　design　mode　resulting　in　the　highest　efficiency　for　multimodal　VIV　mitigation.　The　performance-based　multimodal　VIV　mitigation　design　can　be　realized　with　three　parameters,　i.e.,　inertance　ratio,　damping　coefficient,　and　stiffness　coefficient.　Moreover,　the　performance-based　multimodal　VIV　mitigation　approach　and　models　proposed　in　this　study　demonstrate　a　high　level　of　precision.　©　2024　The　Authors