  In this paper we construct families of bounded domains $\Omega_\varepsilon$
and solutions $u_\varepsilon$ of \[\begin{cases} -\Delta u_\varepsilon=1&\text{
in }\ \Omega_\varepsilon\\ u_\varepsilon=0&\text{ on }\
\partial\Omega_\varepsilon \end{cases}\] such that, for any integer $k\ge2$,
$u_\varepsilon$ admits at least $k$ maxima points for small enough
$\varepsilon$. The domain $\Omega_\varepsilon$ is "not far" to be convex in the
sense that it is starshaped, the curvature of $\partial\Omega_\varepsilon$
vanishes at exactly $two$ points and the minimum of the curvature of
$\partial\Omega_\varepsilon$ goes to $0$ as $\varepsilon\to0$.
