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Discover LudwigThe phrase 'suppose further' is correct and can be used in written English.
You can use it when you are trying to make a more detailed hypothetical statement or assumption. For example: "Suppose further that the company has a good track record and offers competitive salaries."
Exact(60)
Suppose further that you expect more than a little resistance.
Suppose further that nobody in the industry experiences a major security breach for a couple years.
Suppose further that each ant can move 10 cm per second.
Suppose further that he used the Fed's research staff to document these facts.
Suppose it's close, and suppose, further, that Ohio makes the difference.
By Jeffrey Toobin November 5, 2012 Suppose it's close, and suppose, further, that Ohio makes the difference.
Suppose further that this school only offers six different courses from which the students select four to take.
Suppose further that, instead of being teachers, they had jobs with no social standing - estate agents or even journalists.
Suppose further, that all flesh came together into a single whole of flesh endowed with this aquiline quality.
Suppose further that it was one that, in your heart, you expected and felt entitled to win.
Suppose further that public health officials in New York and Washington succeed in forcing food companies to use less salt.
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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