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"supplement by" is a correct and usable phrase in written English, usually used to mean to add or increase something.
Example: We need to supplement our current financial resources by seeking out investors.
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A feeding and digestion study was completed to determine whether sodium bicarbonate supplementation modifies diet selection of whole barley grain and a protein supplement by lambs.
He was among players unwittingly given a supplement by Tour trainers that contained nandrolone.
She said she had been sent the supplement by the Balco subsidiary from 1999 to early 2001.
But he supported a failed amendment that would have paid for the supplement by repealing tax cuts for the wealthy.
She undertook a detailed analysis of Burchfield's supplement, comparing it with the 1933 supplement by Charles Onions and William Craigie.
Melatonin, which is produced at night, helps regulate sleep and is often taken, as a supplement, by long-haul travellers.
The Latvian-made drug, which is typically prescribed for heart conditions, was widely used as a supplement by athletes in eastern European countries.
When the words along the creases began to vanish, we bought additional spelling books, including "Valerie's Spelling Bee Supplement," by a legendary trio of spelling sisters.
I tried some pay-what-you-can yoga and dance classes, but the best supplement by far was simply walking home from work.
Their five-dollar fee for each Choir! participant provides them with a very small income, which they supplement by holding Choir! sessions and teaching the group's values at corporate retreats and in office settings.
The arrests, made Tuesday, coincided with the publication of a special supplement by the newspaper, Shargh, that paid homage to Student Day, the annual commemoration of the deaths of student protesters in 1953.
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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