I think I know the answer to my question, and that answer is no. But I have to ask.
Is it possible to establish a base component out of an existing set of component variants? I assume this is impossible due to the way components are engineered. It would probably be a bit like creating a mother out of a child.
The reason I want to do this is that my team has a few component sets that could benefit from having a base component. I prefer to not start from scratch with a new base component because there are hundreds of instances of the component variants throughout our design files.