"Art at cross purposes" is not a word or phrase that has antonyms. This is because "art at cross purposes" is an idiomatic expression that means different people pursuing different goals or objectives, leading to confusion, conflict, and failure. Antonyms usually refer to words that have opposite meanings. However, we can look for synonyms of "art at cross purposes" to get a better understanding of the expression. Some of the synonyms include conflict of interest, discord, disharmony, dissension, misunderstanding, and lack of coordination. By understanding the opposite meanings of these synonyms, we can better appreciate the essence of "art at cross purposes.