Whenever a List version of another tagged value type is suggested my response is always to use multiple tagged values. (Which I consider to be multiple values for the one property)
In my view (and experience), "There be dragons!"
We have enough trouble keeping notionally single tags in check. Something, even after a decade we haven't figured out what, (and see below) creates either identical duplicates or semantically equivalent tags - so we can't tell which are real multiples and which are spurious.
So, we early on adopted the rule that ALL tags are singular. We wrote queries to locate and eliminate the duplicates. Thus we could preserve the semantic integrity of the repository. As a consequence, trying to locate the duplicate generator has dropped significantly in priority. We suspect problems with the Tags collection mechanisms, but there is no proof.
In our case, if the set is of values that correspond to elements that we have in the repository (and we have many elements conforming to what others might see as merely Set members) then we use RefGuidLists - the repository defines the Set.
It seems to me that you only need one more Tag type to accommodate just about all requirements for Set related lists:
Type=Set;
Members=First,Second,Third;
Default=«Uninitialized»;
And bingo! most requirements are satisfied.
Paolo