He worries more [than is necessary].
Might I trouble you to tell me whether or not 'than is necessary' is a relative clause modifying 'more'?
No. The than clause is a complement of more - it completes its meaning.
I suppose that semantically its function is similar to a non-restrictive relative clause; but
1) Than is not a relative pronoun (or a relative anything else)
2) The head of a relative clause is almost always a noun (or noun phrase), not an adjective or adverb.