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Discover Ludwig"otherwise engaged" is a correct and usable phrase in written English.
You can use it to indicate that someone or something is busy or occupied elsewhere and therefore can't attend or isn't available. For example, "The meeting won't be attended by the CEO, he is otherwise engaged."
Exact(56)
Romantically they're both otherwise engaged.
SERVICE Sullen and "otherwise engaged".
And if you're lucky, they'll be otherwise engaged.
The danger seemed reasonably imminent, and their parents otherwise engaged.
Redknapp was otherwise engaged Wednesday, fighting in court.
In fact, I expect most residents are probably otherwise engaged.
Some of us are otherwise engaged at 10am on weekdays.
Or rather she would so cradle us, if both hands were not otherwise engaged.
The author, having enlisted in the army, was otherwise engaged, and inattentive to these concerns.
Some of these figures are distracted dreamers tucked in a corner or behind furniture, otherwise engaged.
"She said nothing then, her lovely mouth otherwise engaged, until he came, all over her face.
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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