Technically, that would be eight-boxing. (Or 24 if you let the prize be in any box). I'll explain:

Let's say the prize is in box A. So the eight options are:

• {EY picks box A, host opens box B, EY switches}
• {EY picks box A, host opens box B, EY doesn't switch}
• {EY picks box A, host opens box C, EY switches}
• {EY picks box A, host opens box C, EY doesn't switch}
• {EY picks box B, host opens box C, EY switches}
• {EY picks box B, host opens box C, EY doesn't switch}
• {EY picks box C, host opens box B, EY switches}
• {EY picks box C, host opens box B, EY doesn't switch}

By symmetry, there are eight options for whichever box it is in, so there are 24 possibilities if you include everything.