Fact with more than one relation to the same dimension in the same role

I'm having trouble getting my wits around this. I have a Market dimension and a particular fact, the way the OLTP source is designed, can be in more than one Market, say US and AL. But it is not necessarily a hierarchy. I wouldn't want to use roles and have a Market1Key and Market2Key and I don't think I want a US/AL market key. Is there a standard solution for something like this?

A bridge table is the standard solution if the number of references is not known or have no 'status' (for lack of a better word).

The 1, 2 thing doesn't work well even if there are a fixed number of references as they are difficult to use together. It only works if there is a clear precedence, an use of multiple references is not common.