We analyze the response of molecular adhesion complexes to increasing pulling forces (dynamic force spectroscopy) when dissociation can occur along either one of two alternative trajectories in the underlying multidimensional energy landscape. A great diversity of behaviors (e.g. non-monotonicity) is found for the unbinding force and time as a function of the rate at which the pulling force is increased. We highlight an intrinsic difficulty in unambiguously determining the features of the energy landscape from single-molecule pulling experiments. We also suggest a class of ``harpoon'' stickers that bind easily but resist strong pulling efficiently.