I might could do that.

source: 
LAGS
Entry: 
421
Example: 
I might could do that.
Modal 1: 
might
Modal 2: 
could
Gender: 
Male
Race/Ethnicity: 
White
Age: 
27
Level of Education: 
Graduate school (Master's degree)
Home Community, Town, or State: 
AL (Troy)
Location Collected: 
AL (Troy)
Year: 
1977
Relation to Addressee: 
subject to fieldworker
Medium: 
Spoken
Sentence Structure: 
1.0
Status: 
Naturalistic