We study both experimentally and theoretically the driven motion of domain walls in extended amorphous magnetic films patterned with a periodic array of asymmetric holes. We find two crossed-ratchet effects of opposite sign that change the preferred sense for domain wall propagation, depending on whether a flat or a kinked wall is moving. By solving numerically a simple phi(4) model we show that the essential physical ingredients for this effect are quite generic and could be realized in other experimental systems involving elastic interfaces moving in multidimensional ratchet potentials.