It is a regular source of amazement, the things people will be amazed by.
For example, it was our privilege the other day to publish a letter to the Arkansas Democrat Gazette from one of our valued correspondents. The letter was a model of brevity. It was also a thorough provocation to any defender of the mother tongue in these parts, aka Suthuhn.
To quote the letter, in toto:
"I was utterly amazed to see Œthe board might could use a little guidance' in a recent editorial. Might could use? What English grammar book did that come from? Shame on you. Your Arkie background is showing."
Ooo-wee. My reactions came fast and a little furious. First came a not very nice question: "You're not from around here, are you, friend?"
Second, I've never been ashamed of showing my Arkie background. I do, after all, work for Arkansas' statewide newspaper. My problem has been the opposite: trying to control my hair-trigger pride in Arkansas, which used to be known as the Wonder State long before we changed our license plates to read The Natural State.
Third and more to the point, when we asserted that a public board "might could use a little guidance," we did so - if you'll forgive my lapsing into English Teacher Mode - to modify the more definite, "could use a little guidance." There's a slight but significant difference in the two grammatical constructions for those who take pains with their language. At the time this board seemed to be on its way to realizing and correcting its mistakes, but we couldn't be sure. Hence, it might could have used some guidance.
Think about it. Suppose you're asking some old boy to undertake a job for you, like digging a drainage ditch or putting a new clutch in your old rattletrap. If he says, "I could do it," you've probably got yourself a deal. On the other hand, if his response is, "I might could do it," the negotiations have just gotten a mite more complex.
One of the great advantages of a regional dialect is that it's rooted in real life and real distinctions, like the one between "I could" and "I might could," each with a different degree of probability. To sacrifice such shades of meaning for no better reason than a false respectability is to lose sight of what language ought to be about: conveying meaning precisely, even about imprecision.
As for what grammar book I learned this construction from, the answer is: none. I picked it up by ear, by experience, from life, which can be even more instructive than a formal text. And usually is.