  In this paper we show how some known weak forms of the Zilber--Pink
conjecture can be strengthened by combining them with the Mordell--Lang
conjecture or its variants. We illustrate this idea by proving some theorems on
atypical intersections in the semiabelian and modular settings. Given a
"finitely generated" set $\Gamma$ with a certain structure, we consider
$\Gamma$-special subvarieties -- weakly special subvarieties containing a point
of $\Gamma$ -- and show that every variety $V$ contains only finitely many
maximal $\Gamma$-atypical subvarieties, i.e. atypical intersections of $V$ with
$\Gamma$-special varieties the weakly special closures of which are
$\Gamma$-special.
