That's actually a cool idea for a password manager in general. After logging in, you input a "salt" value that is appended to the end of all your passwords. That value is never sent to the password server, so even if the server is compromised your associated accounts aren't.

There's actually a name for that: pepper

Instead of a salt, which is random for each entry and has to be stored along the hash, one single pepper is added to each password before hashing and kept secret.