Damped outrigger is a viable means for reducing dynamic responses of tall buildings. This study focuses on generalized damped outrigger (GDO) systems. A GDO is composed of a damper for energy dissipation, a negative stiffness device and an inerter for damping enhancement. The GDO system incorporates GDOs at different floors of the tall building optimized to varied structural modes. Frequency equation of a tall building simplified as a cantilever beam with multiple GDOs is first derived by complex modal analysis. A finite different model of such a system is used for verification. Parametric analyses are then performed to compare damping effects of different GDO systems. It is found that a negative stiffness damped outrigger (NSDO) or inerter damped outrigger (IDO) needs to be optimized for maximizing damping of a specific mode. GDOs, respectively, tuned to different modes can largely improve the multimode damping effects. The optimal parameters of the GDOs are slightly different from those in the case when they are installed separately. With both negative stiffness and nonzero inertance, a GDO still needs to be tuned to a specific mode because multimode damping is sensitive to the damper coefficient. The combination of an NSDO optimized to the first mode and an IDO tuned to a higher mode seems the best solution. The IDO additionally improves the first mode damping provided by the NSDO and the two-mode damping is not sensitive to the damper coefficient of the NSDO. The findings are confirmed through seismic response analyses of a tall building with different GDO systems.