Is it possible for a DP like "three times" to act as an AdvP ("He read the book three times.")? How would such a constituency tree look like? How does the DP modify the verb? Conversely, would the same thing apply to constructions in Dutch such as "twee keer"?
Is it possible for a DP like "three times" to act as an AdvP ("He read the book three times.")?
You're confusing terminology here.
The DP loosely "acts as an AdvP" in the sense that it's modifying the VP, but that isn't because it's actually acting as an AdvP. It's because AdvP and DP can both adjoin to a verb to modify it according to the semantic function they carry. When you adjoin a DP, it doesn't become an AdvP, or act as one; it just becomes an adjunct and acts as one.
If you consider PP adjuncts—which you probably already know about—it's exactly the same thing. A PP doesn't become an AdvP when it's an adjunct instead of an argument. Neither does a DP.
How would such a constituency tree look like?
That depends on your favorite theoretical analysis of adjuncts. Presumably you're looking for an MP analysis, given that you're asking about DP rather than NP. But whatever you like, draw your favorite version of the tree for "He read the book repeatedly", then just sub the DP in for the AdvP, and you're done.
For example (ignoring whatever is above the VP, and whether it has anything in spec), if you analyze [VP^ read the book [AdvP^ repeatedly]] like this:
… then you analyze [VP^ read the book [DP^ three times]] like this:
Conversely, would the same thing apply to constructions in Dutch such as "twee keer"?
I don't know Dutch, but if this is a valid sentence (Google seems to think it is):
- Hij las het boek drie keer.
… then yes, the VP is presumably structured the same way: [DP het book] is the complement of the verb, and [DP drie keer] an adjunct.
In fact, you can go way beyond close relatives to English and find DP adjuncts as frequency modifiers. (That's what makes people think that adjunction is part of Universal Grammar in the first place.) For example, in Japanese:
- Kare wa so-no pon o san-kai yon desu.
- He topic-particle that-genitive-particle book accusative-particle three-occurrences read do.
- He read the book three times.
The [DP san-kai] doesn't take the -ku ending (sort of similar to English -ly, but fully regular and productive) that an adjective/adverb would take here, so it clearly isn't an AdvP, but it is adjoining and modifying the same way.