Nature is providing particles with energies exceeding 100 EeV. Their existence imposes immediate questions: Are they ordinary particles, accelerated in extreme astrophysical environments, or are they annihilation or decay products of super-heavy dark matter or other exotic objects? If the particles are accelerated in extreme astrophysical environments, are their sources related to those of high-energy neutrinos, gamma rays, and/or gravitational waves, such as the recently observed mergers of compact objects? The particles can also be used to study physics processes at extreme energies; is Lorentz invariance still valid? Are the particles interacting according to the Standard Model or are there new physics processes? The particles can be used to study hadronic interactions (QCD) in the kinematic forward direction; what is the cross section of protons at center-of-mass energies √ > 100 TeV? These questions are addressed at present by installations like the Telescope Array and the Pierre Auger Observatory. After the year 2030, a next-generation observatory will be needed to study the physics and properties of the highest-energy particles in Nature, building on the knowledge harvested from the existing observatories. It should have an aperture at least an order of magnitude bigger than the existing observatories. Recently, more than 200 scientists from around the world came together to discuss the future of the field of multi-messenger astroparticle physics beyond the year 2030. Ideas have been discussed towards the physics case and possible scenarios for detection concepts of the Global Cosmic Ray Observatory -GCOS. A synopsis of the key results discussed during the brainstorming workshop will be presented.