So I'm still not sure I totally get the objection -- please help me out here. In my mind, multiple hierarchies are represented by a single graph.

When one reasons about the system, one will naturally only consider single hierarchies at a time for simplicity. The way to do this is center yourself on a node at a time, and then from that vantage point, traverse the node in different directions.

In the system, each edge belongs to only 3 categories: P ("parent", directed), A ("associate", undirected), S ("source", directed). We're only considering hierarchies, so we'll restrict ourselves to "P". Each node can have an arbitrary number of relationships with other nodes. A family and work relationship could look like this.

You -P-> your kid 1

You -P-> your kid 2

Mother -P-> You, Sister

Father -P-> You, Sister

Boss -P-> You

Boss -P-> Colleague

Company President -P-> Boss

Company -P-> Company President

Seems to me it should be easy to reason about multiple parents in different contexts -- they all belong in the same graph.

Wikipedia sort of does this with its Categories box at the bottom of every page, but Wikipedia only has one kind of relationship category: P.