This strange and redundant verb phrase occasionally pops out of the
mouth of older folks from the Southern United States; it has
been known to stun English teachers at fifty paces.
The phrase is
basically a corruption of "Maybe (subject) could..." and is used to
indicate a similar level of uncertainty and doubt. For example, let's say your cousin Jim Bob was supposed to be at your house
at 5:00 to drive your Grandma Riddle home. 5:00 passes, as does 5:30;
there's no sign of Jim and nobody answers the phone at his house. You
need to get Grandma home, but Jim's the only one whose truck isn't up on
blocks in the yard. You're stuck. "Well," says your cousin Maybell, "you
might could call Aunt Gertie...maybe she seen him today bein' that she
lives not ten minutes away."
In this case, the use of "might could" indicates that Maybell is
grasping at straws here--she doesn't particularly think that Gertie will
have seen Jim, but doesn't really know what else to propose. In other
regions of the country, she might have said "Maybe you could call Aunt
Gertie" (which would still involve a few extra words) or perhaps "You
could check with Aunt Gertie."
As you might expect, younger Southerners tend to have this term drummed
out of them at an early age so that they don't sound like unbelievable
hicks (and so that the South isn't littered with catatonic English teachers).