Can a being be reborn into more that one body in Tibetan Buddhism?

I was reading that both the Dalai Lama and Karmapa are both rebirths (emanations) of the Bodhisattva Avalokiteśvara . Also there are other lamas who are also emanations of Avalokiteśvara. So is Avalokiteśvara reborn into more than one body and if so is every being that is Avalokiteśvara the same in some way? Or is that just different Tibetan traditions? Generally is rebirth restricted to one body or can it be split across more than one? I appreciate that this will be different across branches of Buddhism so can I restrict my question to Tibetan Buddhism.