  It was shown in Bj\"orn--Bj\"orn--Korte ("Minima of quasisuperminimizers",
Nonlinear Anal. 155 (2017), 264-284) that $u:=\min\{u_1,u_2\}$ is a
$\overline{Q}$-quasisuperminimizer if $u_1$ and $u_2$ are
$Q$-quasisuperminimizers and $\overline{Q}=2Q^2/(Q+1)$. Moreover,
one-dimensional examples therein show that $\overline{Q}$ is close to optimal.
In this paper we give similar examples in higher dimensions. The case when
$u_1$ and $u_2$ have different quasisuperminimizing constants is considered as
well.
