Is it possible to have a password prompt that directs users to different pages?

What I’d like is to have one password prompt that directs different users to different pages on my site depending on which password they enter. For example, I could tell some people that the password is “sweet”, and some people that the password is “sour”. Those who entered “sweet” as a password would be directed to one page, Cakes, on my site, while those who entered “sour” would be directed to the page Soups. Someone who entered neither would be denied entry.

Is this at all possible, using any plugin that currently exists?