multiple parent categories

I've seen this topic come up in several places on the internet, so in addition to it being a question I thought it might be a useful discussion as well.

I'm developing a taxonomy management system in PHP & MySQL. One of the features I want to implement is allowing categories to have multiple parent categories. The way I implement this will depend on the conditions under which a category would need multiple parents.

From studying the Amazon.ca taxonomy structure as well as some others I've found categories with multiple parents in three situations:

1. Browsing Habits: Some categories show up in more than one place based on where visitors are likely to look in order to find them, or based on their popularity. "Christian Books & Bibles" is a subcategory of "Religion & Spirituality" but it is also a main category due to its relative popularity over the other religious categories.

2. Inversion: Amazon's "Gay & Lesbian" category has a subcategory of "History". It also has a "History" category with a subcategory of "Gay & Lesbian". Same category, different aliases, and simply switching around the parent-child relationship. Ultimately I think this is just a variation of number 1.

3. Taxonomy Mixing: Personally I think this one should be avoided as a matter of best practice. But one example that I saw in a post somewhere had to do with "German" blog posts being a subcategory of both "European Union" as well as "Language". I think this one should be avoided by using two mutually exclusive taxonomies (Say, Regional and Language). There's no guarantee that a German language post is going to be something about Germany, or that a post about Germany is going to be in German. Not unless the specific nature of this said blog guaranteed that these two conditions would always be met. In which case it would be a second variation on number 1.

So my question is, is there a fourth? These are all the conditions I can think of for categories to have multiple parents. Can anyone think of any other concrete examples where a category could fit with equal relevance under different parents?
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