Yes! Qualifiers often have their own noun groups inside them.
You could highlight each thing, classifier, pointer and so on in the qualifier. The downside is you’d lose the sense of the qualifier as a complete unit, so unless we specifically need to, we’ll highlight a qualifier as a single piece, no matter how long it gets.
To learn more about this, check out the prepositional phrases lesson. Qualifiers are often prepositional phrases, and they can get wild.