Hi Ken,
There's no direct way of doing this, but would be possible if you write some code as a workaround.
I would recommend not using Enum and instead use a Ring Control, as this gives you the flexibility of adding items to the 'list' during run-time. You will need to make use of a property node in order to update the list with new entries. You will probably need to have one permanent entry that the user can click on, and this would invoke the code required to add a new item to the list and update the 'new' array. If I get time, I'll try to create an example, but can't promise. Which version of LV are you using.
With LV8.0 an XControl could be used to make the functionality more professional as well as creating your own Control short-cut menus etc.