This article explains/describes Southern American English (SAE) in great detail.  Here’s the part that blew my mind:

Other grammatical features are less widely known but are no less important. SAE also modifies the English auxiliary system by allowing for the use of more than one modal in a verb phrase. For instance, for most Southerners “I might could leave work early today” is a grammatically acceptable sentence. It translates roughly as “I might be able to leave work early,” but might could conveys a greater sense of tentativeness than might be able does. The use of multiple modals provides Southerners with a politeness strategy not available in other regional dialects. Although no generally agreed upon list of acceptable multiple modals exists, the first modal in the sequence must be might or may, while the second is usually could, can, would, will,should, or oughta. In addition, SAE allows at least one triple modal option (might shouldoughta) and permits useta to precede a modal as well (e.g., “I useta could do that”).

Uh, I might could understand this if I’d paid better attention in 10th grade English.