FWIW there seems to be a read-only solution, but the write part doesn't appear to work:

• If you create an .oo3 document in a Dropbox folder,
• create an alias to it (Ctrl-Click 'Make Alias'),
• and copy the the alias to:
  ~/Library/Application Support/OmniOutliner 3/Clippings
• (renaming the alias to end with .oo3)
• (and relaunching OmniOutliner and other apps)

You will be able to open the Dropbox files through File > Open clippings, but they don't, in fact, seem to receive the clippings through the services commands

(though there is no warning of failure - arguably a bug ?)

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