  High-energy astrophysical neutrinos, discovered by IceCube, are now regularly
observed, albeit at a low rate due to their low flux. As a result, open
questions about high-energy neutrino astrophysics and particle physics remain
limited by statistics at best, or unanswered at worst. Fortunately, this
situation will improve soon: in the next few years, a host of new neutrino
telescopes, currently under planning and construction, will come online. It is
natural to combine their collected observing power: we propose the Planetary
Neutrino Monitoring System (PLE$\nu$M), a concept for a global repository of
high-energy neutrino observations, in order to finally give firm answers to
open questions. PLE$\nu$M will reach up to four times the exposure available
today by combining the exposures of current and future neutrino telescopes
distributed around the world -- IceCube, IceCube-Gen2, Baikal-GVD, KM3NeT, and
P-ONE. Depending on the declination and spectral index, PLE$\nu$M will improve
the sensitivity to astrophysical neutrinos by up to two orders of magnitude. We
present first estimates on the capability of PLE$\nu$M to discover Galactic and
extragalactic sources of astrophysical neutrinos and to characterize the
diffuse flux of high-energy neutrinos in unprecedented detail.
