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The phrase "a strong base of" is correct and usable in written English
It can be used to describe a solid foundation or support for an idea, argument, or organization. Example: "The success of the project relies on a strong base of research and data analysis."
Exact(54)
That's not to say the governor doesn't have a strong base of support here.
His lineage gives him a strong base of support among China's ruling families.
Fortunately, there is a strong base of knowledge to build on.
We have felt there is a strong base of talent in the metropolitan region.
He has a strong base of support in Sadr City, a slum of two million people in northeastern Baghdad.
"AdvancePCS has built a strong base of managed-care customers while Caremark Rx has focused on the employer marketplace".
A strong base of councillors gives parties the infrastructure and local prominence to campaign effectively in general elections.
Milwaukee is a fine city with a strong base of sports fans, in a state that loves hockey.
Sadr City has been a strong base of support for the rebel cleric Moktada al-Sadr and his Mahdi Army militia.
It helped him establish a strong base of support in the provincial cities from which to stage a powerful challenge for the presidency last year against Mr. Fujimori.
With a strong base of support across northern New Mexico and a Clintonesque lust for campaigning, Mr. Richardson had won eight terms to Congress, always with comfortable margins.
More suggestions(17)
a solid base of
a strong site of
a powerful base of
a strong basis of
a substantial base of
a strong dose of
a strong supporter of
a natural base of
a ready base of
a strong opponent of
a strong tradition of
a meaningful base of
a strong statement of
a bounded base of
a strong advocate of
a strong selection of
a strong feature of
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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