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The phrase "across one another" is correct and usable in written English.
It can be used to describe interactions or relationships between two or more entities, often implying a mutual or reciprocal action.
Example: "The two teams communicated across one another to ensure a smooth collaboration on the project."
Alternatives: "between each other" or "among one another".
Exact(23)
With the help of her son, Clayton, she gets these animals, which weigh 450 to 700 pounds, to behave like kittens or puppies -- rolling over, jumping across one another's backs, standing up on their haunches.
The credits show thinly sliced images of New York gliding across one another — a neat enough way to suggest a town on the go.
The slippery feeling caused by soap reflects the ease with which the layers slide across one another.
Inside the muscle fibers, the signal stimulates the flow of calcium which causes the thick and thin myofilaments to slide across one another.
Scenes shifted filmily across one another, characters slipped in and out of view, the effect being of something not fully told, yet fully present; not quite visible, yet producing a troubled enchantment.
Such terrain appears extraordinarily rugged and highly deformed in radar images, and in some instances it displays several different trends of parallel ridges and troughs that cut across one another at a wide range of angles.
Similar(37)
1. Sit across from one another.
Beyonce showed her insured tush to the crowd, while notables from across the spectrum kissed one anothers'.
Seated across from one another on sofa chairs, the four of us would talk for hours, interrupted by only the barking of the senator's Portuguese water dogs.
Some can even eavesdrop on one another across classes.
That airport even staged a changing-of-the-guard ceremony in Terminal B on Thursday, with members of both groups staring across at one another in tight formation.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com