Context. The accretion of pre-main sequence (PMS) stars is a key process in stellar formation that governs mass assembly, influences angular momentum conservation and stellar internal structure, and shapes disc evolution, which serves as the birthplace of exoplanets. Classical T Tauri stars (cTTSs), low-mass PMS stars actively accreting from a disc, hold a well-described magnetospheric accretion model. Their strong, inclined dipole magnetic fields truncate the disc at a few stellar radii, channelling material along magnetic field lines to fall onto the stellar surface near the dipole pole. However, this paradigm assumes the presence of a single star, and a complete description of the accretion process in multiple systems remains to be achieved.

Aims. Building on our previous work on DQ Tau and AK Sco, our aim is to describe the accretion processes in cTTS binaries, accounting for the influence of stellar magnetic fields. Specifically, we explored how the magnetospheric accretion model of cTTSs can be applied to V4046 Sgr, a spectroscopic binary composed of equal-mass and coeval cTTSs in a circular orbit with synchronous rotation, surrounded by a circumbinary disc.

Methods. We analysed a time series of ESPaDOnS spectra covering several orbital cycles. A variability analysis was performed on the radial velocities and on the Balmer, He  i D3, and Ca  ii emission lines, which are associated with the accretion process.

Results. We identified the secondary as the system's main accretor, operating in an unstable regime. Additionally, we detected an accretion funnel flow connecting the dipole pole of the primary star with a nearby bulk of gas.

Conclusions. We concluded that the two components exhibit dissimilar accretion patterns. The primary operates in an ‘ordered chaotic’ regime, where accretion funnel flows and accretion tongues (which penetrate the magnetosphere to reach the stellar equator) coexist. Conversely, the secondary appears to be in a chaotic regime, where the accretion tongues dominate.