Might could do that.

source: 
LAGS
Entry: 
415
Example: 
Might could do that.
Modal 1: 
might
Modal 2: 
could
Gender: 
Male
Race/Ethnicity: 
White
Age: 
27
Level of Education: 
College (Business administration degree)
Home Community, Town, or State: 
AR (Huguley)
Location Collected: 
AR (Lanett)
Year: 
1978
Relation to Addressee: 
subject to fieldworker
Medium: 
Spoken
Sentence Structure: 
1.0
Status: 
Naturalistic