A single particle confined in an asymmetric potential demonstrates an anticipated ratchet effect by drifting along the 'easy' ratchet direction when subjected to non-equilibrium fluctuations. This well-known effect can, however, be dramatically changed if the potential captures several interacting particles. Here we demonstrate that the inter-particle interactions in a chain of repelling particles captured by a ratchet potential can, in a controllable way, lead to multiple drift reversals, with the drift sign alternating from positive to negative as the number of particles per ratchet period changes from odd to even. To demonstrate experimentally the validity of this very general prediction, we performed transport measurements on a.c.-driven vortices trapped in a superconductor by an array of nanometre-scale asymmetric traps. We found that the direction of the vortex drift does undergo multiple reversals as the vortex density is increased, in excellent agreement with the model predictions. This drastic change in the drift behaviour between single- and multi-particle systems can shed some light on the different behaviour of ratchets and biomembranes in two drift regimes: diluted (single particles) and concentrated (interacting particles).