The most recent surveys on the study of the connection between mutual military buildups, arms races, and military interstate disputes (MID) warn of research projects, especially in the case of the Greece-Turkey dyad, that have reached a stalemate. This is due to the difficulty of capturing motivations, which constitute the main variable that turns mutual military buildups into arms races. Using the Greece-Ottoman Empire and Greece-Turkey dyads as proof-of-concept cases, we advance a novel approach for analyzing the interrelation between mutual military buildups, arms races, and MIDs that can overcome that stalemate. We suggest a two-stage approach that focuses on the dyad as a unit of analysis. In the first stage, which we preset here, we use rivalry to divide dyad history into periods of differing subsistence military spending. We then locate periods of mutual military buildups in the different rivalry periods of a dyad history. We argue that this process provides a more nuanced and detailed grasp on the presence of mutual military buildups in a dyad. It also provides the foundation for the future second stage of analysis, where qualitative research can focus on the specific periods of mutual military buildups to unearth indicators of motivation.