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"deeper layer" is correct and can be used in written English.
It can be used when describing something that is composed of different levels or layers. For example: "The deeper layer of the atmosphere is made up of rare gases like helium and argon."
Exact(60)
But there's a deeper layer of uncertainty.
But maybe the real action was in this deeper layer.
"The Simpsons," for instance, with its jovial, animated exterior barely obscures a deeper layer of social satire and allusion.
An ulcer may be superficial, or it may extend into the deeper layer of the skin or other underlying tissue.
When a callus is conical in shape, penetrating into the deeper layer of the skin and causing pain when pressed, it is called a corn.
Fossils in the shale are older than in surrounding sediments, indicating that the shale came from an older, and therefore deeper, layer.
But this idea has lately run across a deeper layer of complexity and one that is only now being outlined in the lab.
Mucous membranes vary in structure, but they all have a surface layer of epithelial cells over a deeper layer of connective tissue.
It is marked by the sudden onset of multiple, red, painful nodules in the deeper layer of the skin on the external surface of the lower legs.
In the disk, the germinal layers develop much as in birds, with the formation of a primitive streak and migration of the chordamesoderm into a deeper layer.
"The Blue Bird" plays the game quite well, but it seems to be reaching for a deeper layer of import that like most of the species these scientists seek, eludes it.
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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