You cannot change enumerations at run time, although this is not specifically mentioned in the reference guide, one could infer it from the text about enumeration keys (https://world.mendix.com/display/refguide4/Enumeration+Values). It is logical however, since Mendix generates forms which can contain cells which are visible for certain enumeration values only. Adding or removing enumeration values would mean these forms have to be generated again, and that is something the business modeler does, instead of the business server.
If you want a drop down list with choices which is editable at run time, you should model it as a entity, and use a reference selector. Then, at run time, you can create objects to populate the list.