Recent investigations of regions of stability for multi-strange hadronic systems, made up of nucleons and hyperons {p, n, Lambda, Xi(0), Xi(-)} are reviewed. Relativistic mean field calculations, designed to reproduce the observed binding energies of ordinary nuclei and of Lambda, Xi and Lambda Lambda hypernuclei, predict a large class of such objects which are stable against strong decay, including the bulk limit A --> infinity, with binding energies per baryon as large as E(B)/A similar to -22 MeV, large strangeness per baryon f(s) similar to 1-1.2, small charge per baryon f(q) similar to -0.1 to 0 and with baryon densities 2-3 times that of ordinary nuclear matter. A straightforward extension of the Bethe-Weizsacker mass formula into the strange domain accounts satisfactorily for all of these features.