The study of mechanical unfolding, through the combined efforts of atomic force microscopy and simulation, is yielding fresh insights into the free-energy landscapes of proteins. Thus far, experiments have been mostly analyzed with one-dimensional models of the free-energy landscape. We show that as the two ends of a protein, filamin, are pulled apart at a speed tending to zero, the measured mechanical strength plateaus at similar to 30 pN instead of going toward zero, deviating from the Bell model. The deviation can only be explained by a switch between parallel pathways. Insightful analysis of mechanical unfolding kinetics needs to account for the multidimensionality of the free-energy landscapes of proteins, which are crucial for understanding the behavior of proteins under the small forces experienced in vivo.