Thanks for the layers option. I have for instance used it to make a diagram of a data flow, where each business flow is a layer on its own. In this way, it is easy to see and edit each business flow.
Now I want to copy this to another board. 

So I need a feature, where I can mark an area of the board (e.g. a frame) and make a copy of everything, including information about layers. Alternatively, I could mark the layers I want to copy in the Layers panel.

So when I paste it into a new board, I can continue working with the layers.