Let $D$ be an $n$-dimensional integral
domain with $n> 1$ which is not quasi-local,
and let $\Sigma'(D)$ be the set of semistar-operations
on $D$. We show that $\mid\Sigma'(D)\mid \geq n+5$.
Also we answer to a problem posed in [MSi],
and answer to a conjecture posed in [MSu].