Bound nuclear systems with two units of strangeness are still poorly known despite their importance for many strong interaction phenomena. Stored antiprotons beams in the GeV range represent an unparalleled factory for various hyperon-antihyperon pairs. Their outstanding large production probability in antiproton collisions will open the floodgates for a series of new studies of systems which contain two or even more units of strangeness at the PANDA experiment at FAIR. For the first time, high resolution gamma-spectroscopy of doubly strange Lambda Lambda-hypernuclei will be performed, thus complementing measurements of ground state decays of Lambda Lambda-hypernuclei at J-PARC or possible decays of particle unstable hypernuclei in heavy ion reactions. High resolution spectroscopy of multistrange Xi(-) -atoms will be feasible and even the production of Omega(-) -atoms will be within reach. The latter might open the door to the vertical bar S vertical bar = 3 world in strangeness nuclear physics, by the study of the hadronic Omega(-) -nucleus interaction. For the first time it will be possible to study the behavior of Xi(+) in nuclear systems under well controlled conditions.