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Assuming that Otto III survives his illness when he was just 21 y.o. and lives until older age, if he had married Zoë Porphyrogenita as planned IOTL and Zoë becomes Empress of Byzantium as well, he would become Emperor of the HRE ("West Roman Empire") and consort Emperor of the ERE at the same time.

It could have open the chance of a son of Otto and Zoë to inherit both Empires, but it would have been quite challenging situation to manage.
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