Being an MVP does not give you the privilege to doubly accept an answer. Read the help for Answers. It tells you what privileges are accrued with increasing rep.
As I recall, occasionally two answers can get accepted, if two acceptances are registered at the same time, before the database knows what has happened. The OP can always accept an answer immediately. Once accepted, that locks other answers out from being accepted.
If the OP has not accepted an answer within 7 days, then all answers are opened up for acceptance, by users with sufficient site rep. (500 rep is all that is needed, based on the rep privileges listed in the help.) I gather this is when a double acceptance can rarely occur, if then TWO answers are accepted within a sufficiently short span of time.