Copy view mode custom settings
There isn't any built in way of doing this. I'm sure you could make a custom module that could do this, but it wont exactly be trivial.

What makes this a bit tricky, is that the information is store many different places. Each field has it's weight stored in the field_config_instance table, which holds general information about the field, like widget settings etc. The weights for all the extra fields for the entity/bundle is saved as a key to the field_bundle_settings variable that can be accessed with variable_get.

If you want to explore this you can take a look at the field_ui_display_overview_form_submit function which is responsible for saving the display info.