One century data of τ CMa: a (2+1)+1 system with a short-period overcontact binary and an eccentric intermediate orbit with probably no apsidal motion

τ Canis Majoris (CMa) is an intriguing system that has captured astronomers' attention for more than a century. The two main components Aa and Ab are two evolved O stars on a 350 years orbit. Aa is itself a SB1 with a 155-days period and a 0.3 eccentricity. Since Hipparcos, we know that a 1.28-days period eclipsing binary (EB) is hidden somewhere in Aa or Ab, but nowhere else. Our recent analysis finally disentangles the system. We calculated the visual Aa-Ab orbit from AstraLux imaging. We detected the SB2 nature of Aa based on STIS spectra, the companion of the O star (Aa1) being a B+B binary (Aa2 = Aa2a + Aa2b). Multiple lines of evidence point towards Aa2 being the EB: time delays in the eclipsing orbit detected by TESS, high mass for Aa2 from SB1 from constraints from the orbit of Aa1, and a lack of radial-velocity motion of Ab synchronised with the eclipsing orbit. This remains as a tentative conclusion pending further analysis. We detect secular changes in the SB1 orbit of Aa1 on a baseline longer than a century. At this stage, the effect is most likely caused by the change in velocity of the Aa center of mass due to the Aa-Ab visual orbit. Apsidal motion is most probably not the culprit.