If a being on a planet experiences infinite expansion of mass, starting from zero, will there come a point that the planet might revolve around him?

A thought experiment that I would like to work into a story. Need to basically know the tipping point of such an event happening.
Assumption: The being is starting from a small size and is still alive & functioning even with the square-cube law in effect

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If a being on a planet experiences infinite expansion of mass, starting from zero, will there come a point that the planet might revolve around him?

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