The phrase "team all-around competition" refers to a competitive event where teams compete in multiple categories, such as gymnastics or figure skating. But there are many synonyms for this phrase. For example, it can be called a "team multi-discipline competition," a "team all-around tournament," or a "team multi-event showdown." Some other potential synonyms include a "group multi-sport challenge," a "team variety competition," or a "team all-rounder contest." No matter what you call it, the spirit of these events is one of teamwork, strategy, and skill, as teams work together and push themselves to excel in a variety of different disciplines.