  We give a flexible method for constructing a wide variety of limits of
betweenness relations. This unifies work of Adeleke, who constructed a Jordan
group preserving a limit of betweenness relations, and Bhattacharjee and
Macpherson who gave an alternative method using a Fra\"ss\'e-type construction.
A key ingredient in their work is the notion of a tree of B-sets. We employ
this, and extend its use to a wider class of examples.
