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Discover LudwigThe phrase "cross purposes" is correct and frequently used in written English.
It is typically used to describe a situation where two or more people have different goals or intentions that conflict with each other. Example: The team's efforts were constantly at cross purposes, with each member pursuing their own agenda instead of working together towards a common goal. You can also use "at cross purposes" to indicate that someone is unintentionally working against someone else's goals. Example: Mary and John were both trying to plan a surprise party for their friend, but they were at cross purposes and ended up accidentally inviting the same people twice. Overall, "cross purposes" is a useful phrase for describing conflicts or misunderstandings among individuals or groups with different agendas.
Dictionary
cross purposes
noun
Plural of cross purpose
Exact(26)
The two men talk at cross purposes.
"I'm at cross purposes," he lamented.
Goodman then wrote: "Apols – cross purposes.
Information and meaning work at cross purposes.
The whole society operates at cross purposes.
Moreover, some older policies work at cross purposes.
Similar(34)
We're at cross-purposes.
The two elements seem at cross-purposes.
Two men talk at cross-purposes.
Either way, you are at cross-purposes.
Are the princes working at cross-purposes?
More suggestions(2)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com