Is there a name for the set of possible ***direct*** answers to a question?

Look at the definition of semiotic schema described in this book.

The schema includes a description of possibilities, it describes the actual sign tokens by describing which other sign types could have been produced instead.

It's pretty abstract and convoluted, but it seems to be on track with what you're looking for.

In computer networking, the term could be called a response schema.

In mathematics, it would be called the codomain.

https://en.wikipedia.org/wiki/Codomain

All, of course, are technical terms that are field-specific, but depending on what you want to this term for, you may be able to appropriate the terms for your use.