At this time it is not possible to sync multiple Dropbox Business accounts to one computer at once, unless the above workaround you correctly mentioned is used. What can be done, however, is to connect a Business and a personal account on one desktop application.
This way you can easily switch between the two without having to log out of the app or the computer user profile.
Thank you for your feedback and interest though - I have forwarded it along to our team for reference!
Let me know if I can help with anything else moving forwards.
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