We propose a methodological approach for a comprehensive and total probabilistic tsunami hazard assessment (TotPTHA), in which many different possible source types concur to the definition of the total tsunami hazard at given target sites. In a multi-hazard and multi-risk perspective, the approach allows us to consider all possible tsunamigenic sources (seismic events, slides, volcanic eruptions, asteroids, etc.). In this respect, we also formally introduce and discuss the treatment of interaction/cascade effects in the TotPTHA analysis and we demonstrate how the triggering events may induce significant temporary variations in short-term analysis of the tsunami hazard. In two target sites (the city of Naples and the island of Ischia in Italy) we prove the feasibility of the TotPTHA methodology in the multi-source case considering near submarine seismic sources and submarine mass failures in the study area. The TotPTHA indicated that the tsunami hazard increases significantly by considering both the potential submarine mass failures and the submarine seismic events. Finally, the importance of the source interactions is evaluated by applying a triggering seismic event that causes relevant changes in the short-term TotPTHA
