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If there are many files opened it is very hard to see and navigate between them. I would like to suggest having tabs to extend to a second line (or more) when needed.
You can use the sidebar to show the opened files. Go to Edit -> Preferences -> Interface -> Sidebar and click "show documents list". Now in the sidebar you have a documents tab. Click it and you'll see the tabs. If you don't want to show the complete path of the file, right click on the sidebar and uncheck "show path" :)
That is certainly useful as an alternate method, but I do think multiple rows of tabs would still be very useful (if only because you wouldn’t have to choose between selecting among documents and code symbols), especially for people like me who use Geany in portrait mode.