Base-isolated buildings are typically important facilities that are expected to remain functional after a major earthquake. Seismically isolated buildings can experience large displacements at the isolation level during strong earthquake excitations, which can exceed the rattle space clearance and potentially cause pounding against the moat wall. The impact can transfer large accelerations to the superstructure, which can damage both structural and nonstructural components. To accommodate such large displacements, a sufficiently wide clearance must be provided around the building and the surrounding moat wall. However, the width of the seismic gap is limited by practical and architectural constraints, as well as associated costs. Additionally, for existing buildings, the available clearance may not be sufficient given the evolution of the seismic hazard characterization. One solution to reduce the isolation system lateral displacement with a focus on its velocity is to place viscous dampers at the isolation interface. However, providing constant damping through viscous dampers may increase the force of the superstructure, especially for ULS earthquakes where displacement reduction is not necessary. A D3 viscous damper can provide damping in any desirable quadrants, and therefore, this type of damper can be tailored to improve the performance of the isolated building by providing force only at critical displacement and recentering the isolation system. This paper explores the seismic performance enhancement of a base-isolated building provided with D3 viscous dampers. The results show that using D3 viscous dampers could reduce the instances of moat wall contact and residual displacement for large earthquakes without reducing the performance of the base isolation during moderate earthquakes.