Currently, when using PlatformUI there is no option to copy the whole subtree of Content Objects. Only the single Content Object can be copied.

The API provides the option to do that from the Location Service: https://github.com/ezsystems/ezpublish-kernel/blob/413f4074c5ebe66e22c46685e9f894b404379a56/eZ/Publish/API/Repository/LocationService.php#L37.