Might can.

source: 
LAGS
Entry: 
285
Example: 
Might can.
Modal 1: 
might
Modal 2: 
can
Gender: 
Female
Race/Ethnicity: 
White
Age: 
55
Level of Education: 
College
Home Community, Town, or State: 
GA (Newnan)
Location Collected: 
GA (Newnan)
Year: 
1976
Relation to Addressee: 
subject to fieldworker
Medium: 
Spoken
Sentence Structure: 
unknown
Status: 
Naturalistic