You can walk your way up the ancestor tag chain by continuing to call getParent() on whatever is returned by getParent(). Because getParent() returns either another tag (on which you can call getParent()), or null.
In a JSP
<mine:NestedLevel> <mine:NestedLevel> <mine:NestedLevel/> </mine:NestedLevel> </mine:NestedLevel>
In a Classic tag handler
Result
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