Tunneling spectra for individual atoms and dimers of Mn and Cr adsorbed on superconducting Pb thin films were measured by a low temperature scanning tunneling microscope. Multiple-resonance structures within the superconducting gap on the adsorbates were resolved and interpreted as the magnetic impurity-induced bound states associated with different scattering channels. The experiment demonstrates a spectroscopic approach to characterizing the spin states of magnetic structures and exploring the competition between superconductivity and magnetism at the nanometer scale.