Map of maps is actually a tree-type structure without single root node (as well as map of maps of maps...).
You can look at Composite pattern which is widely used for implementing tree structures (if their components has the same type which is not the case as I feel).
Another solution is to implement a simple domain model. It'll be much clearer to read and easy to maintain something like:
school.getPupil ("John Doe").getMark ("Math")
than
school.get ("John Doe").get ("Math")
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