Fishing for Complements?

Hi, everybody,

I have a language with clause initial particles that make for VERY flexible
word order.

The subject of a clause is the last argument of the verb, the argument that
gets the most clause stress, and the only argument that can be deleted.
The subject also identifies the topic of the clause or sentence.

However, the subject can be an agent or a patient or a bunch of other
things, depending on the clause-initial particle.

Similarly, the argument that comes before the subject can be an agent,
patient, or a bunch of other things, depending on the clause-initial
particle.

QUESTION:    What do I call the argument that comes before the subject?   I
need a syntactic term, and "object" just won't cut it;   after all, "object"
suggests that the argument can't be an agent.

I thought about just calling it a "complement."

But won't that be too easily confused with the complement of an adposition,
the complement of a linking verb, or the kind of clause that can fill a noun
phrase slot?

I'm reluctant to use the term "complement," because it has too many other
uses already.

What should I call my extra argument?    (I'll keep working on that, but any
suggestions will be welcome.)

Jim