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Then there’s the “royalist or not, it’s hard not to be moved by this celebration of the Queen” approach, which seems to include younger people wanting to partake of some – partly manufactured – collective feeling.

The Guardian.

Is “royalist or not, it’s hard not to be moved by this celebration of the Queen” a modifier in the NP?

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anonymousIs “royalist or not, it’s hard not to be moved by this celebration of the Queen” a modifier in the NP?

It modifies "approach" adjectivally.

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anonymousIs “royalist or not, it’s hard not to be moved by this celebration of the Queen” a modifier in the NP?

Assuming you're taking "approach" as the head of this NP, yes.

CJ