I've been able to work this out, and I don't need to enumerate at all.
It turns out that the reason I had this question in the first place is because I was trying implement OOP improperly.
The derived classes need to employ various techniques
specific to themselves to store elements (probably strings representing field names, in this case) from which the abstract class can build a SQL statement and send it to the backend data class.
See how simple it is when it's done correctly? <g>