We introduce the concept of modified vertical Weil functors on the category F2Mm 1 ,m 2 of fibered-fibered manifolds with (m1, m2) -dimensional bases and their local fibered-fibered maps with local fibered diffeomorphisms as base maps. We then describe all fiber product preserving bundle functors on F2Mm 1 ,m 2 in terms of modified vertical Weil functors.