When talking about a group of individuals or organizations who are pitted against each other, essentially competing towards a shared goal, the term "team overall competition" might be used. Some synonyms for this phrase could include "group rivalry," "collective contest," or "team-wide challenge." Other possible options might be "multi-team competition," "organized playoff," or "tournament-style battle." Ultimately, the choice of words used to describe such a scenario will depend on various factors, such as the language style or cultural context of the conversation or written work. Regardless, the underlying meaning of individuals or groups competing with one another remains the same.