When you install larger, oversized wheels on a vehicle, you significnatly increase the weight of the wheel/tire assembly. This means the stock springs and shocks and sway bard may not be stiff enough to control the extra weight.
My advice would be to replace the stock shocks with some adjustable aftermarket shocks (like Koni shocks). I would also recommend replacing the stock sway bars with larger, stiffer aftermarket sway bars. You might also consider slioghtly stiffer springs, too, but all of these changes to improve vehicle stability will probably make your Explorer ride rougher, too.