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The phrase "a much greater slice" is correct and usable in written English.
It can be used when discussing a larger portion or share of something, often in a comparative context.
Example: "In the latest budget proposal, the education sector received a much greater slice of funding than in previous years."
Alternatives: "a significantly larger portion" or "a far bigger share".
Exact(1)
Wages still account for a much greater slice of income than profits, but labour's share has been in decline across the OECD since 1980.
Similar(59)
These observations indicate that ethanol suppresses LTP in the adolescent hippocampus at concentrations that do not affect than it suppresses in the adult slices, suggesting a much greater sensitivity to ethanol in adolescence.
It has a much greater decorative effect.
Posey had a much greater impact Thursday.
The enemy took a much greater loss.
Sanitation is a much greater challenge.
If David Haye follows his gambling instincts tonight and unleashes something dangerous but special on Nikolai Valuev, the real prize will be much greater than a quarter slice of a world title.
Thus, signals can be captured from a greater slice of the sky.
We want the workforce to take home a greater slice of the Sainsbury's pie.
In addition to the challenge of growing revenue, clubs are arguing for a greater slice of the existing pie.
You gain control of a much bigger slice of the media pie.
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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