We have developed a formalism for microscopic Brueckner-type calculations o
f dense nuclear matter that includes all types of baryon-baryon interaction
s and allows us to treat any asymmetry in the fractions of the different sp
ecies (n, p, Lambda, Sigma(-), Sigma(0), Sigma(+), Xi(-), and Xi(0)). We pr
esent results for the different single-particle potentials, focusing on sit
uations that can be relevant in future microscopic studies of beta-stable n
eutron star matter with strangeness. We find that both the hyperon-nucleon
and hyperon-hyperon interactions play a non-negligible role in determining
the chemical potentials of the different species.