We have developed a formalism for microscopic Brueckner-type calculations of dense nuclear matter that includes all types of baryon-baryon interactions and allows to treat any asymmetry on the fractions of the different species (n, p, $\Lambda$, $\Sigma^0$, $\Sigma^+$, $\Sigma^-$, $\Xi^-$ and $\Xi^0$). We present results for the different single-particle potentials focussing on situations that can be relevant in future microscopic studies of beta-stable neutron star matter with strangeness. We find the both the hyperon-nucleon and hyperon-hyperon interactions play a non-negligible role in determining the chemical potentials of the different species.