The double modal is a construction primarily associated with Southern American and Texan English, where two modals (helping verbs that don’t get conjugated, like may, might, could, etc.) are used. (Standard English only allows for one modal in a verb phrase.)
The best-known of these double modals is might could — meaning something like might be able to — and in fact this particular usage appears to have spread across the U.S. by now. However, double modals do not appear to generalize into other American Englishes; might would and especially might should remain mostly restricted to the South. This suggests that might could has been borrowed into other American Englishes as an idiom, rather than as a change to the underlying grammatical structure.