NON EMPTY CROSSJOIN With Multiple Levels of a Single Dimenision

I need to do a NON EMPTY  CROSSJOIN where I need to return data from multiple levels of 2 dimensions.  When I try to run this, I get this error "Formula Error - duplicate dimension across (independent) axes in a <set> ..."  An example of the structure is below:

SELECT {[Measures].[Sales],[Measures].[Transactions]} on columns ,    
NON EMPTY  CROSSJOIN(CROSSJOIN({[Region].[Level 1].Members},  {[Region].[Level 2].Members}  ), {[Region].[Level 3].Members})
ON rows  
WHERE ([Time].[2008].[Quarter 4].[October].[1])


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Better to use parent (or parent.parent) and a local calculation to get the name of parent. Simple solution that has minimal performace overhead and you get what you want - names of the levels for some members of the same hierarchy.
with member measures.CategoryName
[Product].[Product Categories].CurrentMember.Parent.Parent.Name
member measures.SubcategoryName
[Product].[Product Categories].CurrentMember.Parent.Name
select {measures.CategoryName, measures.SubcategoryName, measures.defaultmember} on columns,
[Product].[Product Categories].[Product Name].&[456] on rows
from [Adventure Works]

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