Including faults as seismogenic sources in probabilistic seismic hazard assessments (PSHA) has turned into a common practice as knowledge of active faults is improving. Moreover, the occurrence of earthquakes in multi-fault ruptures has evidenced the need to understand faults as interacting systems rather than independent sources. We present a PSHA for the Southeastern Spain obtained by including the faults of a moderate seismicity region, the Eastern Betics Shear Zone (EBSZ) in SE Spain, as the main seismogenic sources in two separate source models, one considering background seismicity. In contrast with previous studies in Spain, earthquake occurrence of the EBSZ system is modeled considering different hypotheses of multi-fault ruptures at the whole fault system scale and weighted in a logic tree. We compare the hazard levels with those from an area source PSHA and a previous fault-based approach. The results show a clear control of the EBSZ faults in the seismic hazard for all return periods, increasing drastically the hazard levels in the regions close to the fault traces and influencing up to 20 km farther with respect to the area source PSHA. The seismic hazard is dependent on the fault slip rates as peak ground accelerations and territorial extension of the fault influence appear higher around the Alhama de Murcia and Carboneras faults, while lower slip rate faults (Palomares Fault) show minor contribution to the hazard. For the return period of 475 years and near-fault locations, our models are more consistent with the ground motion values reached in the 2011 Mw 5.2 Lorca event than the building code or national seismic hazard map, which suggest that our fault system-based model performs more accurate estimations for this return period. Fault data, mainly slip rates, and its uncertainties have a clear impact on the seismic hazard and, for some faults, the lack of detailed paleoseismic studies can compromise the reliability of the hazard estimations. This, together with epistemic uncertainties concerning the background seismicity, are key discussion points in the present study, having an impact on further research and aiming to serve as a case example for other low-to-moderate seismicity regions worldwide.