There is no such enclitic, at least not a common one by any measure.
And what would you need it for?
If a question does not ask for a yes or a no, it has a specific question word indicating what is wanted: quis, quando, cur, unde…
As Sebastian says in his answer to the linked question: -ne is not used when we have a question word like quid or ubi.
Enclitics can be used in all questions:
Ubi saltant maritus uxorque?
The enclitic -que is used, but it does not indicate a question.
The only enclitic indicating a question is -ne.
As noted in Sebastian's answer, binary questions can be formed without -ne, using nonne or num.
But when the question is not binary, using -ne is not really an option.