I guess if you wanted to get wild you could do some kind of multiselect picklist and have some formula to mark the fields clay is updating as "true" but that feels like a lot of work.
If I ever put companies (or contacts) into another clay table, I just always pull in all properties and set run conditions to limit any additional column runs/enrichments if I have previously found a certain value. Sometimes I'll have that set in combination with the last enriched date so certain things run again on a regular cadence.