We determine in an extended Brueckner-Hartree-Fock formalism self-cons
istent single-particle potentials of nucleons, lambda, and sigma hyper
ons for a system consisting of symmetric nuclear matter and lambda hyp
erons of uniform densities rho(N) and rho(A), respectively. The bindin
g energy per baryon of this system is discussed and its maximum strang
eness content preserving binding is evaluated. The results are used to
introduce a hyperonic symmetry energy term in a generalized mass form
ula for multistrange hypernuclei.