Can a PP be analysed as a complex adjective?

Solution 1:

We cannot analyze one syntactic form as another one. Each grammatical form is defined by a set of criteria that makes it distinguishable from another one. So, a preposition cannot be an adjective, a noun cannot be a verb etc. Grammatical forms can be distributionally/functionally comparable or similar in certain syntactic contexts, but one cannot be the other. So, my general answer to the title question is no and never.

They are more at home with this.

The whole thing is an ascriptive predicative complement with the form of a prepositional phrase. There is a lot to say about this one. First, there is a number of prepositional phrases which are gradable (completely in control, very much out of sorts, wholly out of order etc. CGEL p643), typically functioning as the predicative complement. In the sentence at hand the adverb "more" modifies the following head PP "at home".

Which brings us to the interesting part. The head of a phrase doesn't have to be a word - it can be another phrase. This is the case here. The head of the PP "more at home with this" is another PP - "at home". The PP "with this" is a complement of the head PP "at home".

The authors of CGEL say "..one PP can function within a larger one, as head, complement, or modifier" (p646), which is followed by sentences illustrating each use.