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The phrase 'expand this argument' is correct and usable in written English.
You can use it when you want to present a more in-depth discussion or analysis of a particular argument. For example, "This article outlines the main points of the argument, but more research is needed to expand this argument."
Exact(2)
To further expand this argument, Latin American development assistance will be presented next.
Many expand this argument by suggesting that RCTs are too simple to adequately assess the complex nature of surgical interventions, and that there may be many factors or complexities about the intervention as a whole that influence outcomes.
Similar(57)
In On the Mystery of the Trinity, Bonaventure expands this line of argument further in the direction of the transcendentals.
Arenberg and co-author Robert Dove expand on this argument in their book, Defending the Filibuster: The Soul of the Senate, which discusses other parts of the Federalist Papers, but makes no mention these crucial Madisonian or Hamiltonian arguments.
Piper, who runs a digital humanities lab at McGill University, in Montreal, expands on this argument in the introduction to his new journal, Cultural Analytics.
She expanded upon this argument five years later in A Vindication of the Rights of Woman.
Mancini complained afterwards about refereeing decisions but was not willing to expand the argument to say that, over the two games, his team deserved to go through.
Hinson et al. (2015) who share similar disposition expand the argument further by suggesting that organisations are pressured to report on their sustainability activities due to institutional and stakeholder influence.
Even if Pulido didn't address the latter in the essay, the map finds a way to expand the argument she begins.
AS THE discussion over Thomas Piketty's new book has expanded, the argument has occasionally been made that concern about inequality is essentially an elite phenomenon.
In book III Socrates expands the argument considerably.
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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