In database systems, a query plan is a series of concrete internal steps to execute a query. Multiple testing approaches utilize query plans for finding bugs. However, query plans are represented in a database-specific manner, so implementing these testing approaches requires a non-trivial effort, hindering their adoption. We envision that a unified query plan representation can facilitate the implementation of these approaches. In this paper, we present an exploratory case study to investigate query plan representations in nine widely-used database systems. Our study shows that query plan representations consist of three conceptual components: operations, properties, and formats, which enable us to design a unified query plan representation. Based on it, existing testing methods can be efficiently adopted, finding 17 previously unknown and unique bugs. Additionally, the unified query plan representation can facilitate other applications. Existing visualization tools can support multiple database systems based on the unified query plan representation with moderate implementation effort, and comparing unified query plans across database systems provides actionable insights to improve their performance. We expect that the unified query plan representation will enable the exploration of additional application scenarios.