Believe it or not, Paul, some of that last little bit did actually make some sense to me because I can see tiniest shadings of different meanings. A lot of it depends, though, on inflection. Let me see if I can wrap my brain around it enough to explain.
First, I would tend to say: What else could I have possibly meant?
It just seems to roll off my tongue more easily.
As for the other examples you use - in the first one, I can see a slight difference in meaning if the inflection is changed as well as the order of the words. And I would change the order along with the inflection:
What could she possibly have meant by that? For me, this sentence implies incredulity and sarcasm. She said something. It was pretty clear what she meant. There is no way to misconstrue it. So, What could she possibly have meant by that? expresses confirmation of the original interpretation.
What could she have possibly meant by that? For me, this sentence asks a serious question. I'm confused. What was she trying to say? No sarcasm implied, but genuine uncertainty.
As for the other two examples, I would always go with "have possibly" so I'm guessing that confirms my US-ishness.
Lynn
You know that boy'd walk on water for you? Or he'd drown tryin'. -Perry White to Lois in Just Say Noah
