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The phrase "a much deeper position" is correct and usable in written English.
It can be used when discussing a more profound or significant stance on a particular issue or topic.
Example: "After further analysis, I realized that my argument was based on a much deeper position than I initially thought."
Alternatives: "a significantly deeper stance" or "a considerably more profound viewpoint."
Exact(1)
As the dose is increased (up to 1×1018 cm−2) in-going yttrium is redistributed almost uniformly within the oxidation scale; when the beam flux is increased the peak of yttrium profile shifts to a much deeper position (245 nm for 76 μA cm−2).
Similar(57)
For example, the epsilon and delta divisions branch from much deeper positions on the phylogenetic tree than do the alpha Proteobacteria.
"We've got a better squad, a much deeper squad at every position, and I think we'll be in a better position to deal with injuries.
"It comes from a much deeper and honest place.
Then something happened that led me to think through my position in a much deeper way.
The Dodgers have a much deeper lineup than a year ago.
That's a much deeper issue".
That could be a sign of a much deeper slowdown.
Today, we are facing a much deeper crisis.
"That is a much deeper and more interesting dynamic".
That could result in a much deeper, more prolonged downturn.
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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