Antonyms for the phrase "are at cross purposes" would be phrases such as "working in harmony" or "on the same page". These phrases refer to individuals or groups that are working together towards common goals and objectives. An antonym could also be "agreeing" or "aligned", which suggests that all parties involved have a clear understanding of what needs to be achieved, and they are actively working towards it in a cooperative manner. In contrast, "are at cross purposes" implies a lack of understanding and coordination, leading to confusion, misunderstandings, and ultimately, inefficiencies. Therefore, the opposite of "are at cross purposes" are phrases that denote cooperation, understanding, and a shared sense of purpose.