systems where the dominant motion is not in the radial direction and the TA therefore significantly underestimates the mass. We therefore make one final cut which requires the approach velocity of the two galaxies to lie between $0.5$ and $1.5$ times the value measured for the real system ($-130{{\rm \,km\,s^{-1}}}$). This results in our final sets of Local Group lookalikes. For the narrower $V_{max}$ range we end up with $117$ pairs when the morphology cut is applied and $758$ pairs when it is not, while for the wider $V_{max}$ range the corresponding numbers are $1,273$ pairs and $8,449$ pairs respectively.

When we study the application of the Timing Argument to the Milky Way–Leo I system, we consider individual galaxies from both our $V_{max}$ ranges. We require these to be isolated by insisting that there should be no bright/massive companion (with luminosity exceeding 10% of that of the host or $V_{max} >
150{{\rm \,km\,s^{-1}}}$) closer than 700 kpc and no massive group (defined as above) closer than 3 Mpc. This produces samples of $137,926$ and $266,229$ potential hosts in the cases with and without the morphology cut for the wider $V_{max}$ range, and $29,245$ and $57,816$ potential hosts for the narrower 