The sub-barrier fusion excitation function of 40Ca + 96Zr has been measured down to cross sections ≃2.4 μb, i.e. two orders of magnitude smaller than obtained in a previous experiment, where the sub-barrier fusion of this system was found to be greatly enhanced with respect to 40Ca + 90Zr, and the need of coupling to transfer channels was suggested relying on coupled-channels calculations. The purpose of this work has been to investigate the behavior of 40Ca + 96Zr fusion far below the barrier, thereby disentangling the elusive interplay of effects due to inelastic couplings, transfer couplings and, possibly, the appearance of the fusion hindrance. The smooth trend of the excitation function has been found to continue, and the logarithmic slope increases very slowly. No indication of hindrance shows up, and a comparison with 48Ca + 96Zr is illuminating in this respect. A new CC analysis of the complete excitation function has been performed, including explicitly one- and two-nucleon Q>0Q>0 transfer channels. Such transfer couplings bring significant cross section enhancements, even at the level of a few μb. Locating the hindrance threshold, if any, in 40Ca + 96Zr would require challenging measurements of cross sections in the sub-μb range.