Accretion and outflows are key processes in early stellar evolution. The material accreted at the edge of the inner disc is channeled along magnetic funnel flows onto the star. Its kinetic energy is dissipated in standing accretion shocks. The accretion process is therefore sensitive to the spatial and temporal variations of the structure of the magnetic field and its mass load. Due to the change of view of the star-disc system throughout the rotation cycle, geometric effects are superimposed on such intrinsic variability and likely dominate the observed variability. An assessment of changes in the mass accretion rate is essential to understand the structure of the star-disc-magnetosphere system. The young, very low-mass star Par-Lup3-4 displays a rich emission-line spectrum, hosts a disc with an almost edge-on inclination, and is in the critical mass range near the star/brown dwarf transition, where the knowledge of the accretion/outflow connection remains rather poor. These properties make this star a prime target for conducting a variability study of mass accretion. We make use of X-shooter's unique capabilities to monitor its broad-band spectrum in the range from ultraviolet to near-infrared. The sampling of our ten spectra covers timescales of hours, days, weeks, and years.