Using a set from one dimension to filter a set on another dimension without using the slicer

I have a complex mdx query.  In one step within this I want to restrict the members of one set to those that have data in the cells defined by this first set and a second set on a different dimension.  It is not the values in those intersection
cells I want to end up with but just the restricted members of the first set.  I am then going to cross join this with the 'All' member of the second set.  The point of doing this is that the results can be joined with a union query to other results
with the same dimensionality.
I get what I want, in simplified way, from the following:
with set x as filter([Org].[Dept].[Dept].members,
[Proj].[ProjHierarchy].[Proj].&[100028])
select [Measures].[Finance] on columns, x on rows from projects
This shows the total finance for each dept member that has any finance against the specified project.  However, this won't do as what is supplied to the mdx is a string parameter that is converted to a list of members using StrToSet and the MDX above won't
accept this.  I do not wish to use the slicer because of the complex overall MDX structure.  Is there any way to make something like the above work?

Hi Kenneth
does this set have the required dimensionality? :
extract(
nonempty(
( [Org].[Dept].[Dept].members
, [Proj].[ProjHierarchy].[Proj].&[100028])
, [Measures].[Finance])
,[Org].[Dept] )
I'm not sure about the hierachy on the last line. Maybe:   [Org].[Dept].[Dept]
Philip,

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