  For a nonzero integer $n$, a set of $m$ distinct nonzero integers
$\{a_1,a_2,...,a_m\}$ such that $a_ia_j+n$ is a perfect square for all $1 \leq
i < j \leq m$, is called a $D(n)$-$m$-tuple. In this paper, we show that there
infinitely many essentially different quadruples which are simultaneously
$D(n_1)$-quadruples and $D(n_2)$-quadruples with $n_1\neq n_2$.
