Geometry for multi-scale graph structure with re-sampling

Question

I recently read a paper that demonstrated the use of a hyperbolic geometric space as a continuous approximation to a discrete tree structure. I'm wondering if there is a similar continuous geometric space to describe a tree-like structure except one in which leaves of the tree can appear in multiple places at the same 'level' in the tree. As a (discrete) example, if I have a concrete set $X = {a, b, c, d, e, f, g, h}$ I want a tree structure that can represent something like this:

Or equivalently thought of as a graph where each node represents a cluster of points such that each point may belong to multiple nodes in the graph. I'm wondering if there's some continuous geometrical space with properties like that.