Complex sentence: Dafoe has been nominated for the Academy Award for Best Supporting Actor twice-for "Platoon" in 1986 and for "Shadow of the Vampire" in 2000.
Split into simpler sentences: Dafoe has been nominated for the Academy Award for Best Supporting Actor twice. The first was for his role in "Platoon" in 1986 and the second time for his performance in "Shadow of the Vampire" in 2000.