  Let $K$ be a multiquadratic extension of $\mathbb{Q}$ and let
$\text{Cl}^{+}(K)$ be its narrow class group. Recently, the authors \cite{KP}
gave a bound for $|\text{Cl}^{+}(K)[2]|$ only in terms of the degree of $K$ and
the number of ramifying primes. In the present work we show that this bound is
sharp in a wide number of cases. Furthermore, we extend this to ray class
groups.
