  For a nonzero integer n, a set of m distinct nonzero integers
{a_1,a_2,...,a_m} such that a_i a_j + n is a perfect square for all 1 <= i < j
<= m, is called a D(n)-m-tuple. In this paper, by using properties of so-called
regular Diophantine m-tuples and certain family of elliptic curves, we show
that there are infinitely many essentially different sets consisting of perfect
squares which are simultaneously D(n_1)-quadruples and D(n_2)-quadruples with
distinct non-zero squares n_1 and n_2.
