Can you performExternalDragDropOfFiles and startDragging at the same time?

I have a case where a use can drag a file, if the drag from my app to my app, I want to use the standard juce drag & drop mechanism, but if they drag to an external window, then I want to do a file drag, is this possible?

You can start the external drag if they drag off the window.
I’m not sure you can get the internal drag back again though.