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The phrase "a slightly higher level of" is correct and usable in written English.
It can be used when comparing degrees or amounts of something, indicating a small increase in intensity, quality, or quantity.
Example: "The new software offers a slightly higher level of security compared to the previous version."
Alternatives: "a marginally increased level of" or "a somewhat elevated level of".
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Today, almost 7 in 10 Americans say they see NATO as "still essential to U.S. security". That is a slightly higher level of support compared with a year ago.
And there were no premieres, just business as usual at perhaps a slightly higher level of excitement.
At a slightly higher level of sophistication, it's an attempt to deny the enemy the positive connotations of its chosen appellation.
Second, if you are up to a slightly higher level of difficulty, just observe your brain as it moves from thing to thing, hunts and pecks.
If it's more complicated, the caller gets bumped up to a second level to an employee who has a slightly higher level of knowledge.
A slightly higher level of abstraction is the gate level that refers to the ability to describe the circuit as a netlist of primitive logic gates and functions.
A slightly higher level of expression of recombinant bFSH subunits was achieved by using the Saccharomyces cerevisiae-derived calnexin (ScCne1) as a chaperone in engineered H. polymorpha strains.
It wants to cut the lowest tax rate from 14% to 12% and to introduce the top rate at a slightly higher level of income.
It will also mean, in Germany as elsewhere, getting used to living with a slightly higher level of risk, as Britain did through decades of IRA terrorism, without losing its liberal bearings.
A slightly higher level of agreement was found between the subjective ratings and the minimum hardness objective values than with the average or maximum values.
For instance, the principle implies that for any population consisting of very good lives there is a better population consisting of just one person leading a life at a slightly higher level of well-being (Parfit 1984 chapter 19).
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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