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The part of the sentence "that allow both" is correct and usable in written English.
It typically is used to express that two different entities are allowed to do the same thing or use the same resource. For example: The restaurant offers two different types of entrees that allow both vegetarians and meat-eaters to enjoy the meal.
Exact(48)
"How can we create the policies that allow both the environment and the economy to flourish?
Experimental conditions are determined that allow both to achieve trap saturation and to avoid stimulated emission.
Natural landing trajectories that allow both minimum-velocity local-vertical touchdown and deployment from a safe distance are investigated.
What Israel should do now is work for a cease-fire on terms that allow both sides to save some face.
Current and future parents need more fluid roles that allow both genders to care for their families in the ways they need it most.
Twitter signed lucrative deals with Google and Microsoft's Bing search service in October that allow both companies to include tweets from Twitter's database in their search results.
Similar(12)
"That's the bonus on top that allows both of them to really flourish," Hackett said.
The most likely outcome still remains a fudge that allows both sides to claim victory.
Usually these disputes are eventually settled by a compromise that allows both sides to claim victory.
Resolution came in the form of linguistic ambiguity that allowed both sides to claim victory.
It was a piece of political craftsmanship that allowed both Democrats and Republicans to declare victory.
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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