Cauvery River, in the southern part of India, has experienced conflict about the right to use water for the last 130 years. Historically, the states/provinces in conflict have used the water from the river for agricultural purposes. In our research, we are developing a novel system of systems approach which takes in scenario-based methods for analyzing the conflict. We have employed four methodologies which feed into each other and overlap, namely, an expert elicitation, an integrated water resources management approach to generate the stream-flow requirements in the basin, a socio-political and economic impact approach which analyses the various relevant factors affecting the conflict in the region, and finally, a graph model to map out the progression of the conflict to potentially resolve. We present our methods and the preliminary findings in this paper.