"At cross purposes" refers to a situation where individuals or groups have conflicting or opposing goals, plans, or opinions. Some antonyms for this phrase could include "aligned," "collaborating," "cooperating," "harmonizing," "in sync," "united," "working together," or "on the same page." These words suggest a sense of unity, agreement, and synchronization among individuals or groups, highlighting their ability to work towards a common goal or objective without any misunderstandings or disagreements. Using such antonyms might be useful when attempting to promote teamwork, collaboration, and cooperation in different areas of life, such as the workplace, relationships, or social contexts.