Where did you come across it? It could mean that the speaker has more than one copy of the Rolling Stones albums.
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EyeSeeYouSo if I said "I've watched that film three times over", it would mean three times as well,Yes, it would mean three times.
EyeSeeYouor is it more related to the notion of having two or more copies of something?No. Not more related. It can be related in either way — times or copies.