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The phrase "a larger slice" is correct and usable in written English.
It can be used when discussing proportions, shares, or segments of something, often in a metaphorical sense.
Example: "In the new budget proposal, we are requesting a larger slice of the funding to support our community programs."
Alternatives: "a bigger portion" or "a greater share".
Exact(56)
They feel they deserve a larger slice of the pie.
Not that character actors don't yearn occasionally for a larger slice of pie.
EASYJET is making a play for a larger slice of the business-travel market.
Being the third-largest smartphone manufacturer in the world, it wants a larger slice of the high-end market.
But plenty of companies, including Crane's, would like to see a larger slice of that eight per cent.
The clubs believe they generate the majority of FFA's revenue and are therefore entitled to a larger slice of it.
Still, universities, professional associations and private institutions are increasingly devoting a larger slice of the pie to the field.
Similar(4)
That's a large slice of working Britain.
Clearly, a large slice of corporate America agrees with him.
Portraiture accounts for a large slice of material.
A large slice of global trade is counted in dollars.
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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