The flexible multi-state switch (FMSS), as a new generation of flexible interconnection device, enables flexible interconnection between different feeders in distribution networks by replacing traditional tie switches. However, the influence of zero-sequence current on the stable operation of the FMSS under asymmetrical fault conditions has not been fully considered in existing research on FMSS control mode transitions. This leads to AC oscillation in the DC voltage before the asymmetrical fault is cleared. To address this issue, a multi-mode control transition strategy based on zero-sequence suppression is proposed for flexible interconnection devices. Firstly, the smooth transition between PQ control mode and U_dcQ control mode during faults is improved by the introduction of a steady-state inverse model. Subsequently, the smooth transition among PQ control mode, U_dcQ control mode, and Vf droop control mode during faults is improved by the introduction of state tracking control. Finally, the impact of the zero-sequence current component on the DC voltage during asymmetrical faults is reduced by the introduction of a zero-sequence current suppression strategy based on a proportional resorant (PR) regulator. A three-port FMSS simulation model is established in MATLAB/Simulink to verify the proposed control strategy. Simulation results demonstrate that the proposed control mode transition strategy effectively reduces DC voltage fluctuation and AC voltage/current phase offset under various fault conditions.