Sorting a dimension attribute by another dimension attribute in SQL Server Analysis Services

SQL Server Analysis Services - SSAS - sorts dimension attributes alphabetically by default. The tip Change Sort Options on Dimension Attributes in SQL Server Analysis Services explains how you can change this sort order by adjusting the key columns and by sorting on this newly created key. A good example is sorting months chronologically instead of alphabetically. But what if you want to sort a dimension attribute by something that cannot be represented in the key? How do you handle this situation?