The answer is no.

There does not exist a book that refers to all and only those books that do not refer to themselves.

Suppose there is a B that refers to all an only those X that do not refer to X.

Then B refers to B if and only if B does not refer to B, which is a contradiction.

So there is no B that refers to all and only those X that do not refer to X.

It doesn't matter what 2-place property you choose ('refer', 'knows', 'shaves' 'is a member of', whatever). For any 2-place property P, we have

There does not exist a b such that for all x, Pbx if and only if ~Pxx.