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The phrase "a supplementary project" is correct and usable in written English.
It can be used when referring to an additional project that complements or enhances a primary project.
Example: "The team is currently working on a supplementary project that aims to improve the overall user experience of the main application."
Alternatives: "an additional project" or "a complementary project".
Exact(1)
QUAL- qual denotes a core project and a supplementary project whereby the latter cannot be a stand-alone project.
Similar(59)
It offers a different –a supplementary– set of standards".
Project Business, a supplementary program for middle school students, was followed in 1981 by Applied Economics, a comprehensive economics curriculum for high school students.
This month the government adopted a supplementary budget that allocates $35.4 billion for projects including a high-speed telecommunications network linking schools.
The project materials also include a supplementary curriculum on such topics as tropical rain forests and the geography of Africa.
The source code of the project is also available as a supplementary file.
Part B is a supplementary insurance that covers outpatient services.
Eventually, Quinn hopes to create a supplementary newspaper comic strip.
Fishing is a supplementary activity.
This file contains Supplementary Methods, a Supplementary Discussion, Supplementary Table 1 and Supplementary References.
Many people do this as a supplementary income.
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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