There are several synonyms that can be used in place of the phrase "sit on top of." One common option is "perch," which suggests a sense of balance and stability. Another is "rest on," which can be used to describe objects that are not necessarily being sat on, but are still placed on top of something else. "Loom over" can add a sense of height or dominance, while "occupy" emphasizes the sense of physical presence. "Ride," "straddle," and "mount" all suggest a more active, intentional placement on top of something. Overall, there are many ways to describe the act of being on top of something, each with its own connotations and nuances.