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You still are able to override Asset display settings after embedding Asset into CKEditor.
All optional fields from the Asset entity type and Display settings can be modified without any impact on the original Asset.
Just call the context menu Override Asset by doing right mouse click on the embedded asset zone and do the modifications.
If user, who embeds Asset has a permission to modify original Asset, he will see "Edit Asset" button, which will open Edit Asset interface. Note that modification of required field in the original Asset will cause an update of display of this Asset everywhere, where this Asset is embedded.
Also "Cut Asset" and "Remove Asset" buttons are available in the context menu.