Assuming that the "default" society type would need an option for megacorps, perhaps even called "Megacorporation", it could perhaps be possible to even move the choice of corporate play from authority/government type selection to the choice of society type. It would fit thematically, and by separating the choice of authority from the choice of corporate play, corporate empires would no longer by default be stuck in an essentially oligarchic position, and could make other choices. There could then also be imperial, dictatorial, and democratic megacorporations.
(Though the same effect could also be achieved by just adding corporate equivalents for those authority types.)
(Though the same effect could also be achieved by just adding corporate equivalents for those authority types.)