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Large-scale multi-directional real-time hybrid simulations (RTHS) are used to assess the maximum considered earthquake (MCE) seismic performance of a 40-story steel building equipped with supplemental nonlinear viscous dampers. These dampers are placed between outrigger trusses and the perimeter columns of a building that was part of the inventory for the California Tall Building Initiative (TBI) PEER study. The analytical substructure for the RTHS consists of a 3-D nonlinear model of the building while the experimental substructure consists of a full scale nonlinear viscous damper. Other dampers in the structure are analytically modelled using an online explicit model updating scheme where the physical damper is used to obtain the parameters of the analytical damper models during the RTHS. The displacement, residual drift, and ductility demand are found to be reduced by adding the dampers to the outrigger, but only in the direction of the plane of the outriggers. Higher modes, including torsional modes, contribute to the 3-D seismic response.