In the last two decades considerable attention has been paid to the dimension theory of self-affine sets. In the case of the generalized 4-corner sets (that is the functions of the IFS generating the set map the unit square into itself in diagonally affine way into the corners) the IFS obtain as the projection of the self-affine system have maps of common fixed points. In this talk we are going to show a formula for the Box-dimension of diagonally self-affine systems in general. Moreover, we calculate the Hausdorff- and Box-dimension of the attractor iterated function systems with non-distinct fixed points. By these formulas we are able to calculate the Box-dimension of generalized 4-corner set for Lebesgue almost every contracting parameters.