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Earthquake rupture propagation across step-overs plays a critical role in controlling the extent of multi-fault ruptures and the final earthquake magnitude. For normal-fault systems, however, the key factors governing rupture-jump potential remain far less investigated than for strike-slip or thrust faults. Assessing rupture behavior in normal fault systems is critical, particularly in tectonically active regions such as Nevada (USA) (Wernicke et al., 1988), the Corinth Rift (Greece) (Bell et al., 2009), the East African Rift System (Ebinger and Sleep, 1998), and the Italian Apennines (Ghisetti and Vezzani, 2002; Faure Walker et al., 2021). These regions are characterized by damaging seismic activity involving multi-segment normal fault ruptures. In segmented fault systems, rupture may initiate on one fault segment (the emitter) and potentially propagate onto a neighboring segment (the receiver) through dynamically evolving stress perturbations. Using a suite of three-dimensional dynamic rupture simulations performed with SeisSol (Gabriel et al., 2025), this study systematically explores the physical conditions that enable rupture jumps across normal-fault step-overs. We examine the influence of pre-stress level, fault spacing, relative fault positioning, and regional stress orientation. Our results show that rupture jumps across gaps of up to 5 km remain dynamically feasible, and that triggered secondary ruptures can evolve into sustained run-away events when fault segments overlap, even at low pre-stress levels. For such cases, the relative positioning between fault segments is fundamental. In contrast, non-overlapping fault configurations restrict successful rupture jumps to distances of less than 3 km. Fault overlap and proximity, however, introduce strong stress-shadowing effects that decrease slip and limit final earthquake magnitudes, revealing a fundamental trade-off between rupture-jump potential and energy release. Fault geometry exerts a first-order control: configurations in which the receiver fault lies within the hanging wall of the emitter fault consistently exhibit higher rupture-jump potential, more frequent sustained secondary ruptures, and larger magnitudes. Comparisons with static Coulomb stress-change predictions demonstrate that static criteria systematically overestimate rupture connectivity, as they fail to capture transient wave interactions, rapid stress reversals, depth-dependent sensitivity, and stopping-phase effects that govern dynamic triggering. These findings highlight the limitations of static stress-based approaches in seismic hazard assessment and underscore the necessity of dynamic modeling to realistically evaluate multi-fault rupture potential in normal-fault systems. These results are partly motivated by the 2016 Amatrice-Norcia earthquake sequence in Central Italy. Our simplified fault configuration is inspired by the geometry of the Monte Vettore and Laga faults, which ruptured in two major events rather than as a single through-going rupture. In this configuration, the presence of a small gap (3-5 km between faults) and the absence of along-strike overlap between segments tend to inhibit rupture jumps, according to our simulations. As a result, dynamically triggered secondary ruptures occur only under favorable conditions and generally leads to self-arrested secondary ruptures. This provides a plausible dynamic explanation for why rupture did not propagate across the entire fault system in a single event, but instead occurred as a sequence of distinct earthquakes.