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The phrase "a further development of" is correct and usable in written English.
It can be used when discussing an advancement or progression of a particular idea, concept, or project.
Example: "The research presented in this paper represents a further development of our previous findings on climate change."
Alternatives: "an additional advancement of" or "a subsequent evolution of".
Exact(59)
Solithromycin is a newly developed fluoroketolide (CEM-101), a further development of the macrolides.
SA is a further development of Grounded Theory, which was developed by Glaser and Strauss in 1967 [ 20].
This is a further development of the successful GOMETRAN.
Radionuclide cineangiography is a further development of radionuclide imaging.
Badminton is a further development of the game.
1149.4, which is a further development of IEEE Std.
Thus, the learning control system is a further development of the adaptive controller.
A further development of the friction-based concept of the deflagration-to-detonation transition is presented.
It is a further development of a quasicombined zero-emission power cycle, published earlier.
Design studies for a further development of the pulse tube engine are performed experimentally.
The last third of "Funny People" is a further development of the question that "Knocked Up" asked: What does it take to be a husband?
More suggestions(15)
a greater development of
a further validation of
a further set of
a further evolution of
a further order of
a further demonstration of
a further role of
a further sign of
a further study of
a further decrease of
a further prediction of
a further implication of
a further type of
a further gesture of
a further sense 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