Observed features of the galaxies in the Magellanic plane might suggest that the Large Magellanic Cloud (LMC) was the largest galaxy in a group of galaxies that entered the Milky Way system at late times. Many of the brightest dwarf galaxies of the Milky Way might be part of this system. Half of the missing satellites might be part of the group, so they survive more easily in such systems than in parent halos as large as the Milky Way. There is further support for such a notion in the properties of the dwarfs in M31 as well as a second possible group that is associated with the Fornax dwarf. We find that the specific angular momentum of the LMC and its group is greater than the disk of the Milky Way and the total angular momentum of the system is comparable to the product of the entire mass of the Milky Way system times the specific angular momentum of the disk. This tilts the angular momentum vector of the Milky Way system by 45 degree and has strong implications for comparing cosmological simulations of angular momentum to present day galaxies.