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Not a good idea IMHO. Typically I would use an interface to specifically define common methods that would be used by multiple implementors... for example, the classic "Save", "Delete", and "Update" methods of my business objects.
I would define the interface with those methods and/or possible overrides of them, and my "customer", "vendor", "order" objects would each implement this common interface. I would instantiate an interface object and then access each implementation object thru this single interface.
If I found myself needing to create an object that "chained" interfaces, it would signify to me that my original interface needs some more methods added to it.
However, since I'm just someone deep in the trenches and I don't have a lot of time for theoretical pursuits, I'm sure a lot of folks may differ with this opinion.