  Each gene has its own evolutionary history which can substantially differ
from the evolutionary histories of other genes. For example, some individual
genes or op-erons can be affected by specific horizontal gene transfer and
recombination events. Thus, the evolutionary history of each gene should be
represented by its own phylogenetic tree which may display different
evolutionary patterns from the species tree that accounts for the main patterns
of vertical descent. The output of traditional consensus tree or supertree
inference methods is a unique consensus tree or supertree. Here, we describe a
new efficient method for inferring multiple alternative consensus trees and
supertrees to best represent the most important evolutionary patterns of a
given set of phylogenetic trees (i.e. additive trees or X-trees). We show how a
specific version of the popular k-means clustering algo-rithm, based on some
interesting properties of the Robinson and Foulds topologi-cal distance, can be
used to partition a given set of trees into one (when the data are homogeneous)
or multiple (when the data are heterogeneous) cluster(s) of trees. We adapt the
popular Cali\'nski-Harabasz, Silhouette, Ball and Hall, and Gap cluster
validity indices to tree clustering with k-means. A special attention is paid
to the relevant but very challenging problem of inferring alternative
supertrees, built from phylogenies constructed for different, but mutually
overlapping, sets of taxa. The use of the Euclidean approximation in the
objective function of the method makes it faster than the existing tree
clustering techniques, and thus per-fectly suitable for the analysis of large
genomic datasets. In this study, we apply it to discover alternative supertrees
characterizing the main patterns of evolution of SARS-CoV-2 and the related
betacoronaviruses
