  We propose a scenario in which the Large Magellanic Cloud (LMC) is on its
second passage around the Milky Way. Using a series of tailored N-body
simulations, we demonstrate that such orbits are consistent with current
observational constraints on the mass distribution and relative velocity of
both galaxies. The previous pericentre passage of the LMC could have occurred
5-10 Gyr ago at a distance >~100 kpc, large enough to retain its current
population of satellites. The perturbations of the Milky Way halo induced by
the LMC look nearly identical to the first-passage scenario, however, the
distribution of LMC debris is considerably broader in the second-passage model.
We examine the likelihood of current and past association with the Magellanic
system for dwarf galaxies in the Local Group, and find that in addition to
10-11 current LMC satellites, it could have brought a further 4-6 galaxies that
have been lost after the first pericentre passage. In particular, four of the
classical dwarfs - Carina, Draco, Fornax and Ursa Minor - each have a ~50%
probability of once belonging to the Magellanic system, thus providing a
possible explanation for the ``plane of satellites'' conundrum.
