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The phrase "an additional degree of" is grammatically correct and commonly used in written English.
It is typically used to emphasize the level or amount of something. Example: "The new policy adds an additional degree of complexity to our already complicated process." In this sentence, "an additional degree of complexity" means that the policy has made the process even more complex than it was before.
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The White House projects that the incremental costs of an additional degree of warming will reach $700bn by 2030.
For each well, an additional degree of freedom is introduced.
Structured multifunctional catalyst particles offer an additional degree of freedom in reactor design.
Such capability offers an additional degree of freedom for designers of nanostructured gas sensors.
The concept simply exploits an additional degree of freedom (DoF) in designing a broadcast MAC.
It exploits the pulse shape as an additional degree of freedom for multicarrier modulation systems.
This brings an additional degree of freedom compared to line commutated switches.
Thus, an additional degree of freedom (DOF) is provided to model crack discontinuities.
The sixth component is computed at the element center and it is enhanced with an additional degree of freedom.
The scheduling model permits recipe changeovers in order to utilize an additional degree of freedom for optimization.
The thermal treatment gives an additional degree of freedom for the design of the optical behavior of the recorded structures.
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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