SU(3) symmetry relations on the recently constructed hyperon-nucleon potentials are used to develop potential models for all possible baryon-baryon interaction channels. The main focus is on the interaction channels with total strangeness S=-2, -3, and -4, for which no experimental data exist yet. The potential models for these channels are based on SU(3) extensions of potential models for the S=0 and S=-1 sectors, which are fitted to experimental data. Although the SU(3) symmetry is not taken to be exact, the S=0 and S=-1 sectors still provide the necessary constraints to fix all free parameters. The potentials for the S=-2, -3, and -4 sectors, therefore, do not contain any additional free parameters, which makes them the first models of this kind. Various properties of the potentials are illustrated by giving results for scattering lengths, bound states, and total cross sections.

22 pages RevTex, 6 postscript figures