1) He laughs at me.
2) He looks downuponon me.
I would avoid the term 'verbal phrase' (or 'phrasal verb'). It is misleading. In your examples it is not the whole expressions "laughs at" and "looks down on" that are verbs; it is just the words "laughs" and "looks".
"Laughs" is best called a prepositional verb, and "looks down on" a verbal idiom.

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