We report here measurements of fusion cross-sections for the ¹⁶O+^112,116 Sn and ³²S+^112,116,120 Sn 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 (≈0.8 V_b to 1.2 V_b) 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.