What proves that speciation is a pairwise process?
I offer this perspective in addition to what WYSIWYG has provided.

Phylogenetic trees are tools to model what has actually happened, or what some evidence implies has happened, to a population of entities that exchange genetic material. 

These models fail, for instance, when describing the phenomenon of horizontal gene transfer since a tree is acyclic by definition. Consider a viral genome that has integrated into a host genome. The host now contains DNA from its ancestral lineage and the viral lineage. This process cannot be modeled by a tree.

Some founder population that is susceptible to exogenous genetic transformation may give rise to many distinct lineages, some of which your species concept may qualify as "new" species.