The obvious example is a time dimension where days roll up by day>month>year but also roll up days>weeks>year. BIDS complains about it, but I see no other way to model the situation.
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You can have more than one hierarchy on a dimension. Your time dimension could have a year-quarter-month-day hierarchy and a year-week-day hierarchy. The hierarchies can share the same 'day' attribute - set up attribute relationships for both of the hierarchies, and 'week' and 'month' can both be attributes of 'day'