The aim of this paper is to present a fractional scaling analysis (FSA) application for a system with interacting components where multiple figures of merits need to be respected during complex transient accident scenario with several consecutive time sequences. This paper presents FSA application to the International Reactor Innovative and Secure (IRIS) reactor and Simulatore Pressurizzato per Esperienze di Sicurezza 3 (SPES3) integral effects test (IET) facility. The FSA was applied for the small break loss of coolant accident (SBLOCA) on the direct vessel injection (DVI) line as the most challenging transient scenario. The FSA methodologies were applied for two figures of merits: (1) reactor and containment vessels pressure responses, and (2) reactor vessel water collapsed level response. The space decomposition was performed first. The reactor vessel and containment vessel were divided in components so that important phenomena and their consequences can be evaluated in each of them. After that, the time decomposition in consecutive time sequences was performed for the considered transient (DVI SBLOCA) based on the starts, or ends, of the defining events. The configuration of the system in each time sequence might be different and dependent on the control system actions connecting, or disconnecting, various components of the system due to the valves openings, or closings. This way, the important phenomena and their consequences can be evaluated for each component and time sequence. Also, this paper presents and discusses options for deriving nondimensional groups and calculation of distortions between prototype and model responses for complex transients containing multiple consecutive time sequences. The input data for scaling analysis are based on the results of RELAP/GOTHIC analysis performed for IRIS and RELAP analysis performed for SPES3. The scaling analysis was applied iteratively several times for different IRIS and SPES3 configurations. Based on the intermediate results, some components in the IRIS and SPES3 were redesigned so that the distortions between IRIS and SPES3 responses are decreased.