We discuss in detail the formation and propagation of multi-strangeness particles in reactions induced by hadron beams relevant for the forthcoming experiments at FAIR. We focus the discussion on the production of the decuplet-particle Ω and study for the first time the production and propagation mechanism of this heavy hyperon inside hadronic environments. The transport calculations show the possibility of Ω-production in the forthcoming PANDA -experiment, which can be achieved with measurable probabilities using high-energy secondary Ξ-beams. We predict cross sections for Ω-production. The theoretical results are important in understanding the hyperon-nucleon and, in particular, the hyperon-hyperon interactions also in the high-strangeness sector. We emphasize the importance of our studies for the research plans at FAIR.