This study, recognizing the game-based structures present in school education, models a 'multi-game structure' in which multiple games are simultaneously being played within the school, and examines its application to specific matters. In the context of preceding research related to the multi-game structure, I reviewed discussions in evolutionary game theory, works by Carse, Suits, Noya, and debates in anthropology. I then illustrated the general form of the multi-game structure, where games with unlimited time and space progress, and games with limited time and space intermittently proceed. Within these games, there may be incompatible elements, or what appears to be the same game may in fact be different games. I discussed instances where the multi-game structure in school education can become problematic. I also discussed cases where different games are played between teachers and students, and incompatible games are played concurrently among teachers. Keyword game-based structure, multi-game structure, finite/infinite game, multiple game situation