Aims. The satellite Linus orbiting the main-belt asteroid (22) Kalliope exhibited mutual occultation and transit events in late 2021. A photometric campaign was organised and observations were undertaken by the TRAPPIST-South, SPECULOOS-Artemis, OWL-Net, and BOAO telescopes, with the goal to further constrain dynamical and photometric models of this sizeable asteroid-satellite system. Methods. Our dynamical model is sufficiently complex, featuring multipoles (up to the order of ℓ = 2), internal tides, and external tides. The model was constrained by astrometry (spanning 2001–2021), occultations, adaptive-optics imaging, and calibrated photometry, as well as relative photometry. Our photometric model was substantially improved. A new precise (<0.1 mmag) light curve algorithm was implemented, based on polygon intersections, which are computed exactly by including partial eclipses and partial visibility of polygons. Moreover, we implemented a ‘cliptracing’ algorithm, again based on polygon intersections, in which partial contributions to individual pixels are computed exactly. Both synthetic light curves and synthetic images then become very smooth. Results. Based on our combined solution, we confirmed the size of Linus, namely, (28 ± 1)km. However, this solution exhibits some tension among the light curves and the PISCO speckle-interferometry dataset, acquired simultaneously with the 2021 events. This indicates that improvements of the shape are still possible. In most solutions, Linus is darker than Kalliope, with the single-scattering albedos A w = 0.40 vs. 0.44. This is confirmed on deconvolved images. A detailed revision of astrometric data has allowed us to revise also the J 2 ≡ − C 20 value of Kalliope. Most importantly, a homogeneous body is excluded. For a differentiated body, two solutions exist: low-oblateness ( C 20 ≃ −0.12), with a spherical iron core, and, alternatively, high-oblateness ( C 20 ≃ −0.22) with an elongated iron core. These values correspond, respectively, to the low- and high-energy collisions we studied via SPH simulations in our previous work.