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The phrase "at a steep" is correct and usable in written English.
It is typically used to describe a high degree or level of something, often in relation to prices, slopes, or changes.
Example: "The prices of the new technology have risen at a steep rate, making it less accessible to consumers."
Alternatives: "at a high" or "at a sharp".
Exact(57)
These successes came at a steep price.
The Boston Globe: sold at a steep loss.
But compliance came at a steep price.
Such contortions came at a steep price.
All of this came at a steep price.
Staying closed on Sundays can come at a steep cost.
For sellers, liquidity comes at a steep cost.
But the security has come at a steep price.
Of course, salvation came at a steep price.
Nevelson did, but it came at a steep price.
Merrill sold the investments at a steep loss.
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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