The AMS-02 experiment measured several secondary-to-primary ratios enabling a detailed study of Galactic cosmic-ray transport. We constrain previously derived benchmark scenarios (based on AMS-02 B/C data only) using other secondary-to-primary ratios, to test the universality of transport and the presence of a low-rigidity diffusion break... We use the 1D thin disc/thick halo propagation model of USINE and a $\chi^2$ minimisation accounting for a covariance matrix of errors (AMS-02 systematics) and nuisance parameters (cross-sections and solar modulation uncertainties). The combined analysis of AMS-02 Li/C, Be/C, and B/C strengthens the case for a diffusion slope of $\delta=0.50\pm 0.03$ with a low-rigidity break or upturn of the diffusion coefficient at GV rigidities. Our simple model can successfully reproduce all considered data (Li/C, Be/C, B/C, N/O, and 3He/4He), although several issues remain: (i) the quantitative agreement depends on the assumptions made on the not well constrained correlation lengths of AMS-02 data systematics; (ii) combined analyses are very sensitive to production cross sections, and we find post-fit values differing by $\sim5-15\%$ from their most likely values (roughly within currently estimated nuclear uncertainties); (iii) two very distinct regions of the parameter space remain viable, either with reacceleration and convection, or with purely diffusive transport. To take full benefit of combined analyses of AMS-02 data, better nuclear data and a better handle on energy correlations in the data systematic are required. AMS-02 data on heavier species are eagerly awaited to further explore cosmic-ray propagation scenarios. (read more)