Wide-area damping controllers (WADCs) have been an effective approach for restraining inter-area low-frequency electromechanical oscillation (LFEO). With the increasing interconnection among different areas of power systems, LFEOs with multiple oscillation modes appear in interconnected power systems. However, the interaction among different oscillation modes has not been fully addressed in previous WADC research, which may potentially deteriorate the control effect of WADC. This paper proposes a coordinated, multi-input, multi-output WADC design method. Interactions among different LFEO modes are considered in the selection of the WADC control loop and tuning of controller parameters, which can ensure the coordination among different controllers for multiple LFEO modes. A subspace method is used to identify the reduced-order model of a power system. After the pre-selection of feedback signals, the control loops of different oscillation modes are coordinately selected through a residue-based method. Furthermore, the residue-based controller design approach is improved to coordinate the parameters of multiple controllers. The case study results in Alberta Power Grid have validated the effectiveness and the advantages of the proposed approach.