Halliday & Matthiessen (2014: 564):
In a hypotactic nominal group complex, the dominant element can, in principle, serve the same function as the whole complex, but dependent elements cannot. Thus instead of have you seen (α) my new hat, (β) with the feather in, we can also say have you seen my new hat, but not have you seen with the feather in. While the dominant element has to be a nominal group, dependent elements can be adverbial groups or prepositional phrases. In nominal group complexing, hypotactic relations are either (i) elaborating, or (ii) extending; but we do not find enhancing ones.