The phrase "three-ring" is typically used to describe a circus with multiple acts happening at the same time. Some synonyms for "three-ring" include "multifaceted," "complex," "complicated," "busy," "hectic," and "varied." These words indicate that there is a lot happening all at once, often creating a sense of chaos or overwhelming activity. Other synonyms for "three-ring" might include "dizzying," "lively," "vibrant," or "energetic." Regardless of the specific synonyms used, the phrase "three-ring" implies a certain level of excitement and activity, making it a useful term for describing busy and dynamic events or situations.