If he's reinstated for two then he can't run a third time.
He certainly can. A President can now serve up to 10 years in office. LBJ could have served 10 years if he had decided to run and won. He finished serving the 2 years of JFK’s presidency when he was assassinated, then 4 more of his own presidency and if he ran, and won would have been 4 more years, for a total of 10.