Salt the hash with something unique to that specific user so identical passwords have different hashes

Isn’t that… the very definition of a Salt? A user-specific known string? Though my understanding is that the salt gets appended to the user-provided password, hashed and then checked against the record, so I wouldn’t say that the hash is salted, but rather the password.

Also using a pepper is good practice in addition to a salt, though the latter is more important.