  We present a conjectured exact formula for overlaps between the Bethe states
of the spin-1/2 XXZ chain and generic two-site states. The result takes the
same form as in the previously known cases: it involves the same ratio of two
Gaudin-like determinants, and a product of single-particle overlap functions,
which can be fixed using a combination of the Quench Action and Quantum
Transfer Matrix methods. Our conjecture is confirmed by numerical data from
exact diagonalization. For one-site states the formula is found to be correct
even in chains with odd length, where existing methods can not be applied. It
is also pointed out, that the ratio of the Gaudin-like determinants plays a
crucial role in the overlap sum rule: it guarantees that in the thermodynamic
limit there remains no $\mathcal{O}(1)$ piece in the Quench Action.
