Might could do that.

source: 
LAGS
Entry: 
416
Example: 
Might could do that.
Modal 1: 
might
Modal 2: 
could
Gender: 
Female
Race/Ethnicity: 
Black
Age: 
76
Level of Education: 
2 days of school
Home Community, Town, or State: 
TN (Fulton)
Location Collected: 
TN (Fulton)
Year: 
1974
Relation to Addressee: 
subject to fieldworker
Medium: 
Spoken
Sentence Structure: 
1.0
Status: 
Naturalistic