  The potential existence of a distant planet ("Planet Nine") in the Solar
system has prompted a re-think about the evolution of planetary systems. As the
Sun transitions from a main sequence star into a white dwarf, Jupiter, Saturn,
Uranus and Neptune are currently assumed to survive in expanded but otherwise
unchanged orbits. However, a sufficiently-distant and sufficiently-massive
extra planet would alter this quiescent end scenario through the combined
effects of Solar giant branch mass loss and Galactic tides. Here, I estimate
bounds for the mass and orbit of a distant extra planet that would incite
future instability in systems with a Sun-like star and giant planets with
masses and orbits equivalent to those of Jupiter, Saturn, Uranus and Neptune. I
find that this boundary is diffuse and strongly dependent on each of the
distant planet's orbital parameters. Nevertheless, I claim that instability
occurs more often than not when the planet is as massive as Jupiter and
harbours a semimajor axis exceeding about 300 au, or has a mass of a
super-Earth and a semimajor axis exceeding about 3000 au. These results hold
for orbital pericentres ranging from 100 to at least 400 au. This instability
scenario might represent a common occurrence, as potentially evidenced by the
ubiquity of metal pollution in white dwarf atmospheres throughout the Galaxy.
