Background: This paper presents the extended-soft-core (ESC) potentials ESC16 for baryon-baryon (BB) channels with total strangeness S = −3 and −4. For these channels no experimental scattering data exist, apart from very recently measured preliminary correlations. Also, there is no information from hypernuclei or hyperonic matter. Purpose: The aim is to calculate the predictions of the ESC16 model for the S = −3 and S = −4 BB channels. Methods: The potential models for S = −3 and −4 are based on SU(3) extensions of potential models for the S = 0 and −1 and S = −2 sectors, which are fitted to experimental data. Flavor SU(3) symmetry is broken "kinematically" by the masses of the baryons and the mesons. The fit to the S = 0 and −1 sectors provides the necessary constraints to fix all free parameters, i.e., baryon-baryon-meson couplings and cutoff masses. The S = −2 systems are constrained by the B value from the Nagara event and the requirement of U ≈ −10 MeV. Results: Various properties of the potentials are illustrated by giving results for scattering lengths, bound states, and phase parameters. Conclusions: No , , and bound states are predicted by the ESC16 model.