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I generally use \newcommand* instead \newcommand whenever it makes sense, to ease error checking if the command doesn't sensibly take multi-paragraph arguments.

Is there a starred version of \DeclareRobustCommand that does the same checking (that it, it makes sure that the arguments to the command are not multi-paragraph)?

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Yes. It works the same way as in \newcommand*:

"4.10 Defining commands" in "LaTeX2e for class and package writers" (clsguide)

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