The hypothesis that the entire cosmic ray spectrum, from <~1 GeV to >~ 100 EeV energy, can be accounted for by diffusive shock acceleration on increasingly large scales is critically examined. Specifically, it is conjectured that Galactic cosmic rays, up to ~ 3 PeV, are mostly produced by local supernova remnants, from which they escape upstream. These cosmic rays initiate a powerful magnetocentrifugal wind, removing disk mass and angular momentum before passing through the Galactic Wind Termination Shock at a radius ~200 kpc, where they can be re-accelerated to account for observed cosmic rays up to ~30 PeV. The cosmic rays transmitted downstream from more powerful termination shocks associated with other galaxies can be further accelerated at Intergalactic Accretion Shocks to the highest energies observed. In this interpretation, the highest rigidity observed particles are protons; the highest energy particles are heavy nuclei, such as iron. A universal "bootstrap" prescription, coupling the energy density of the magnetic turbulence to that of the resonant cosmic rays, is proposed, initially for the highest energy particles escaping far ahead of the shock front and then scattering, successively, lower energy particles downstream. Observable implications of this general scheme relate to the spectrum, composition and sky distribution of Ultra-High-Energy Cosmic Rays, the extragalactic radio background, the Galactic halo magnetic field and Pevatrons.