Good news: with macOS Sierra, this is already available! You can open multiple existing documents in a single window in the shipping OmniOutliner 4 as well as in the latest test builds of OmniOutliner 5.
To see the tab bar, choose View > Show Tab Bar (⇧⌘T). Once you’ve done that, you can drag those tabs from one window to another to arrange them however you like. Or if you’d like to merge all your open documents into a single window, choose Window > Merge All Windows.
If you generally prefer to open your documents in tabs rather than their own separate windows, you can set the Prefer tabs when opening documents setting to Always in System Preferences > Dock.
Hope this helps!
