Advanced Asset contribution / management widget provides next functionalities:

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.

Ok, so you've installed Drupal and gotten it working. You've added a module or two, and maybe you've even changed the theme. Now you want to do more, and adding modules or changing the options doesn't seem to cut it. Maybe you've found that things don't look quite like you want them to, or you want there to be more functionality in a particular module.