I think you final point is key, because I am finding the three-fold ontology (what you have, know or are) to be sufficient. You seem to be trying to create a fourth ontological distinction out of the intersection of "know AND are".

My rule of thumb is that if an idea can be expressed in terms of an existing ontology, it is refinement (perhaps) to expand it, but the expressive power of the enclosing ontology is sufficient.

But I like set theory, and unions and intersections, and saying "ontology" a lot. :-)