No, it is not possible to add enumeration options at runtime. However, following your example, this should not be done using enums in the first place. You should have two associated entities (e.g. Task and TeamMember), and use a reference selector or reference set selector to associate TeamMembers to tasks.
In the domain model snapshot above, one TeamMember can be assigned to many tasks, and one Task will have one TeamMember. If you want to assign multiple TeamMembers to a Task, you need to change the cardinality from 1:n to n:m (many to many).