More and more optical records have exhibited that multiple upward leaders (MULs) occur frequently on a structure in the flash attachment process. An interesting issue is why a structure can continue to launch upward leader (UL) after the first one appears. This phenomenon is analyzed in the present paper. Considering the influence of the leader behaviors on the ambient electric field, an improved 3-D fine-resolution lightning attachment model with MULs is established to simulate cloud-to-ground flash events with diverse leader spatial morphologies. The simulation results show that MULs may initiate almost simultaneously or with an obvious delay and the variation range of UL length is large. From this, the flash events of lightning terminating on a structure are divided into four scenarios and each scenario is analyzed. It can be found that the spatial location of downward leader, the length and propagation direction of the first UL and the time interval from the inception of the first UL to final jump significantly affect the electric fields at top corners of structure and further affect the inception of the second UL. Based on qualitative analysis, four factors are proposed to explain why the above four scenarios happen.