I don’t think so. The logics of adoption are different. Yet the story of Cleveland (just below) suggests that it is possible… while rare.
AV finds favor where the majority can’t agree on the candidate it wants — but can agree on the one it doesn’t. AV is an agreement to passively form coalitions in elections. I say “passively” because the vote-transfer process does the work, likely with help from elite cues.
STV finds favor where the coalition is to be worked out actively, in a legislature. STV also preserves freedom to break the coalition between elections.