I discovered recently that the order of the dimensions in the Applies To defines the order of the dimensions for the drill down too, so you could potentially change it to the most common asked order when drilling down. Note this depends on the Summary method as well, but for line items with "Sum" summary method then it works in a reversed order (i.e. the last dimension in the applies to will appear first in the drill down, and so on). Anyway it's not so dynamic so giving the option to the user to choose which one to drill down on first would be wonderful!
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