The system size dependence of electron acceleration during large-scale magnetic island coalescence is studied via a two-dimensional particle-in-cell simulation. Using a simulation box that is larger than those used in previous studies, injection by merging line acceleration and subsequent reacceleration inside a merged island are found to be the mechanisms for producing the most energetic electrons. This finding and knowledge of the reacceleration process enable us to predict that the high energy end of the electron energy spectrum continues to expand as the merged island size increases. Both the merging line acceleration and the reacceleration within a merged island require the island coalescence process to be so dynamic as to involve fast in-flow toward the center of a merged island. Once this condition is met in an early stage of the coalescence, it is likely to stay in the subsequent phase. In other words, if the thin elongated current sheet is initially able to host the dynamic magnetic island coalescence process, it will be a site where repeated upgrades in the maximum energy of electrons occur in a systematic manner.