The starting point was a recent proposal of Wilkinson’s, his HDoutliers algorithm. The plot above shows the default O3 plot for this method applied to the stackloss dataset. (Detailed explanations of O3 plots are in the OutliersO3 vignettes.) The stackloss dataset is a small example (21 cases and 4 variables) and there is an illuminating and entertaining article (Dodge, 1996) that tells you a lot about it.
Wilkinson’s algorithm finds 6 outliers for the whole dataset (the bottom row of the plot). Overall, for various combinations of variables, 14 of the cases are found to be potential outliers (out of 21!). There are no rows for 11 of the possible 15 combinations of variables because no outliers are found with them. If using a tolerance level of 0.05 seems a little bit lax, using 0.01 finds no outliers at all for any variable combination.