Triple Friction Pendulum Isolators (TFPIs) have been widely used to enhance the seismic capacity of structures in the recent decade. This study intends to measure the effect of different Ground Motion (GM) sets, including Far-Fault (FF) and Near-Fault (NF) records, on the seismic response of the Triple Friction Pendulum (TFP) isolated structures. For this aim, different Engineering Demand Parameters (EDP), including Inter-story Drift Ratio (IDR), absolute floor acceleration, base shear, residual displacement, and damage energy are measured using numerous Nonlinear Time History (NTH) analyses. A three-dimensional mid-rise special moment resisting frames (SMFs) steel building isolated with TFPIs has been designed as per ASCE 7-16. In addition, the separate and simultaneous effect of raising the damping ([Formula: see text]) and the period ([Formula: see text]) of the base isolation system on the seismic responses of the superstructure are measured to assess the structural performance and estimate the damage energy. The [Formula: see text] and the [Formula: see text] are amplified up to 30% and 4.5 times of the superstructure period in incremental steps, respectively. The results show that the damage energy of the superstructure in the Initial Design Parameters' Values (IDPVs) of the isolator under NF records with Forward-Directivity pulses (NF-FD-GMs) is more significant than damping energy, while an inverse trend has occurred for other GM sets. Increasing the IDPVs up to a certain level reduces most EDPs and consequently causes an improvement in the seismic performance of the superstructure. The novel developed empirical relationships can be utilized as useful tools to predict IDRs and the damage states of the superstructure. The variations of the EDPs with respect to simultaneous or separate increasing the IDPVs are also reported for different GM sets.