We report here measurements of fusion cross-sections for the 16O+ 112,116Sn and 32S+ 112,116,120Sn systems. The set of systems studied with widely varying ground state Q values for the transfer of neutrons is a good case to understand the influence of single and multineutron transfer on the fusion process. The evaporation residue cross-sections were measured in small energy steps covering the region around the Coulomb barrier (≈ 0.8Vb to 1.2Vb). The data have been analyzed in the framework of a coupled-channels formalism using the coupled-channels code CCFULL. A comparative study of the 16O+ ASn and 32S+ ASn systems suggests that the fusion process is predominantly influenced by coupling to collective excitations with coupling to multiphonon states (of target and projectile) becoming increasingly important for heavier systems. From the present analysis an unambiguous signature of the role of coupling to neutron transfer channels could not be inferred.