Might could.

source: 
LAGS
Entry: 
442
Example: 
Might could.
Modal 1: 
might
Modal 2: 
could
Gender: 
Male
Race/Ethnicity: 
White
Age: 
24
Level of Education: 
Graduate school (at time of interview; Emory University)
Home Community, Town, or State: 
TN (Chattanooga)
Location Collected: 
TN (Chattanooga)
Year: 
1978
Relation to Addressee: 
subject to fieldworker
Medium: 
Spoken
Sentence Structure: 
unknown
Status: 
Naturalistic