I was able to create a three level unx cascading filter using dimension filters - no scripts, just have to set the members for filtering to 'Only Values with Posted Data' for the second and third level dimension in the initial view.
I was also able to create a two level unx cascading filter using dropdown boxes (the child dropdown being populated by a on select event of the parent dropdown). Not successful with populating the third dropdown via a on select of the second dropdown, though.