Some of this depends on how you want to display your information-- if you want it displayed merely as text, or as measures that can be summed, sorted, and so on.
A quick solution could be treating your measures like text and combining them together:
Sort Value 1
There can be all kinds of problems with this solution, though: you lose the ability to manipulate measures as numbers, plus there are sorting restraints.
Another option you could pursue is GROUPS.
Convert copies of your measures into dimensions, then use the Combine Fields option to generate groups. (Remember, though, that when creating groups, the elements must be selected in the order you want them to appear in the group). Groups can be very useful, and you can refer to them directly in your CASE statement.
A third option is creating three levels of filters:
Filter Level 1
Case [Filter Parameter]
When [Value1] then [Measure 1]
When [Value2] then [Measure 2]
When [Value3] then [Measure 3]
Filter Level 2
When [Value1] then [Measure 11]
When [Value2] then [Measure 21]
Filter Level 3
When [Value2] then [Measure 22]
Drop all three "filter levels" onto your rows or columns as desired. Each field will be populated by the appropriate measure, give a nice columnar view.
One downside of this option is it may leave blank columns when the user has selected only a single value to display.
I hope these suggestions give you some insight to potential solutions. Keep Tableau-ing!