I would punctuate it it like this:
Quote:
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Wasn’t he being a bit of an alpha male—a bit of a king, perhaps?
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The em dash creates a stronger separation than a comma, which makes it a good choice for an aside like "a bit of a king, perhaps". With that said, "a bit of a" seems unnecessarily repetitive, so I would probably change it to:
Quote:
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Wasn’t he being a bit of an alpha male—a king, perhaps?
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or
Quote:
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Wasn’t he being a bit of an alpha male—like a king, perhaps?
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I think the "perhaps" is fine.
Just my $0.02.