The phrase "again defining" is correct and usable in written English.
It can be used when reiterating or clarifying a definition that has been previously mentioned.
Example: "In this section, we are again defining the key terms to ensure clarity for all readers."
Alternatives: "redefining" or "clarifying again".
The result has the welcome feel of philosophical discussion rather than of the major players once again defining their territory.
We here develop analogous design contours for the dynamic problem, based on FORM principles, again defining the contour as a locus of all possible FORM design points.
Within hours, Mattis released a statement once again defining the US objectives minimally – and with clarity atypical of the Trump administration.
The Situationists took up the practice of urban wandering again, defining it "psychogeographical dérive".
In Bogota, Tillerson is expected to hear pleas from Colombian officials who worry that Washington is again defining relations through the prism of security and narcotics.
You could argue that whilst NGO campaigns in Europe and the U.S. are, once again, defining Africa in terms of food shortages, Africa's view of itself is going a different way.
We have one node here, and we can again define that most probable radius.
Almost immediately, however, a new and expanding set of transfers was set up – but again defined as "NHS (health)" spending.
(See, e.g., here and here). What it means to be a private limited company is again defined by statute, as are the UK's eight data protection principles.
He advocates that this level should once again define the Permian-Triassic boundary, since it clearly records a universal geologic event of great significance to marine biotas.
An all-Balanchine program on Tuesday night, highlighted by a powerful performance of "Concerto Barocco," and this season's revival of the 1980 "Ballade" over the weekend at the New York State Theater again defined the distinctiveness of the City Ballet repertory.
