I don't know that I've ever heard a native (American) English speaker use the construction "might could." In my dialect, I would definitely say "might be able to" instead, and "might could" sounds wrong to me. However, I'm pretty sure my professor is a native English speaker, so now I wonder if she might have grown up in a different dialect from my own (I'm from the San Francisco Bay Area). Her pronunciation sounds standard for California, but that doesn't mean too much since most of the western U.S. sounds similar in that respect.
Any thoughts? Native English speakers, what would you say? "Might could" or "might be able to"?