Is there a way to map hierarchies across more than two engagement surveys?

Yes you can do this in current capability. In org hierarchies of participants have you checked hierarchy tools | view org hierarchy action history? Here you selected current project and historical project, mapping any difference in movement.
1) So for your first project you just create a current org hierarchy
2) for a second project you have a new org hierarchy. But you want to map to the first project you need to specify that in the view org hierarchy action history.
3) for each new project you always add your current org hierarchy, then map to your previous org hierarchy.

Once you add each org hierarchy you must update each with current meta data from respective participants. A orange triangle should appear to let you know its updating.

Does that answer your question?

Simonmd14 This helped me narrow down the issue I'm experiencing. It appears that in dashboards the source dataset must be the most recent survey. So If I set up a dashboard on survey A and then conduct survey B and C with the hierarchy mapping you described above, the mapping will not carry through. Instead I need to create a dashboard using survey C as the source dataset in order for the hierarchy mapping to work properly.
Is this correct?

PSimmons Did you manage to resolve your query on hierarchies?