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The phrase "a further level of" is correct and usable in written English.
It can be used when discussing an additional degree or stage of something, often in contexts like analysis, complexity, or hierarchy.
Example: "To fully understand the issue, we need to explore a further level of detail in our research."
Alternatives: "an additional layer of" or "a deeper level of".
Exact(60)
Plant complexes add a further level of value added and begin to add intellectual content.
Often it is seen bathed in a glowing sunset light, which adds a further level of unreality and disorientation.
Trump's lack of preparation has added a further level of unpredictability to his interactions with foreign leaders, the officials said.
The policy of using this drug in force-feeding at Guantánamo adds a further level of horror to what is already a painful and degrading process".
John Pugh, MP for Southport, said: "These are unwanted elected mayors, adding a further level of power that central government can dictate to.
But couched and quiet at its centre is a whole other novel at a further level of knowing, innocence and unsaidness.
These seem to be at once graphic novels, yet not quite comics, creating a further level of ambiguity.
To add a further level of complexity, micropatterned co-cultures were obtained using bovine serum albumin to promote cell adhesion.
Both the national and Community systems are separately encouraging a further level of decentralization, away from administrative and regulatory bodies toward methods of private enforcement.
But that is far less likely to happen with a range of strategies.There is a further level of protection if the manager raises "permanent capital" by issuing shares.
The service that the company was going to offer in Germany could potentially be paid for, in part, by an insurance policy, adding a further level of complexity.
More suggestions(19)
a further level of absurdity
a further category of
a supplementary level of
a complementary level of
a relative level of
a further tier of
a subsequent level of
a significantly level of
a heightened level of
a further cohort of
a deeper level of
a detailed level of
a further layer of
a greater level of
a further decrease of
a further expansion of
a further implication of
a further validation of
a further aim of
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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