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The phrase "a further principle" is correct and usable in written English.
It can be used when introducing an additional guideline or rule that complements previously mentioned principles.
Example: "In addition to the existing guidelines, a further principle must be considered to ensure compliance with the new regulations."
Alternatives: "an additional principle" or "a supplementary principle".
Exact(10)
As the initiative passed from the developers to the Koch administration, a further principle was established.
A further principle was enunciated by Cardinal Bernard Law, archbishop of Boston, in a recent column in his archdiocese's newspaper: "The grave obligation to protect innocent human life must govern our political and military decisions".
This proposition, however, forces the immediate consideration of a further principle, which is that policing, as presently configured, is simply too expensive to be provided as a purely public sector service.
In Justinian's day there was a further principle that in any case of reciprocal agreement, such as an agreement for exchange (but not sale), if one party had performed, he could bring an action to enforce performance by the other.
"What Is Justified Belief?" therefore proposed a further principle to accommodate this additional detail.
Since organs alone are not sufficient to explain animal life, man feels the need to introduce a further principle, which is the soul.
Similar(50)
A further important principle is the rule of substitution of equivalents.
A further plausible principle for the part-of relation is the supplementation principle: if x is part of y, there is an object z that is part of y and that does overlap, that is, have a part in common, with x.
It's not the prettiest solution, but it's a solution, and perhaps the only one that was feasible when so much of the legislating about health care in the U.S. seems to operate on a "this far, but no further" principle, where "this far" is "just enough to create new problems of its own" and "further" is "something that might actually work".
Companies in the public eye should therefore add a further practical principle: abide by the spirit of the times.
A further design principle is to allow for actors taking on different roles of providing and using services across different business domains and value chains.
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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