Take the current structures, but split the "commerce, mobility & transportation" part off of it. Now take these split off-parts and re-assemble them together, not taking borders into considerations, and also have some of them be fully global spanning.
Maybe drop the "corporations" name, just call them "global orgs", since a few of them could also be not-for-profit (but allowed to self-finance, and to maintain forces of self-defense) and handle "global responsibility" issues like oceans pollution, climate issues etc. Other would be for-profit could focus on providing communications infrastructure, people transit security services etc.
In the end the total amount of power could end up even more split up, or maybe a little bit more concentrated but across different borders at different layers (mostly avoiding overlapping the borders of the state level below to the ones of the layers above), some even completely non-physical/non-geographical, maybe "bordered" by different purposefully-non-trivial-to-exchange crypto-currencies.
Sorry if I wasn't clear, the core idea was not "corporations" as we know them, neither concentration of power - just that we'd need self-financing and self-defense-capable trans-national organisms that would be better fitted for providing naturally-global services like communications.