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Discover Ludwig"supplement for" is correct and usable in written English.
You can use it to refer to something (usually a substance) which is added to something else in order to improve it. For example, "Many people take a Vitamin D supplement for their bones."
Exact(60)
Supplement for flights from Edinburgh and Glasgow.
1959 supplement for Economics: an introductory analysis.
"We're acting as a supplement for it".
He recommended a vitamin supplement for Bundy's dog.
Eliminate a "special retirement supplement" for most federal retirees — check.
1963 pocket supplement for Deering's Civil unannotated of California.
Vol. for 1987 has separately published supplement for 10th anniversary.
Computational tools can be a necessary supplement for designers.
A 10% supplement for working one in two weekends a month is a joke.
Well-trained health workers distribute medicine and peanut butter paste, a nutritional supplement for malnourished children.
Excursions are extra, and there is a supplement for the few rooms with a private bathroom.
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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