Rank is not working in multiple dimension filter

And you seem to have created a calculated as 'Dim Selector'[Dimension Selector] isn't aggregated. Calculated columns, unfortunately, do no respond to slicer selections. They are not aware of what's been selected in a slicer.

Instead, create a measure that references the parameter order field otherwise you'll get an error similar to below:

"Parameter columns is part of composite key, but not all columns of the composite key are included in the expression or its dependent expression".

Column switching rank = 
SWITCH (
    SELECTEDVALUE ( DimSelector[DimSelector Order] ),
    0, [Rank by Supplier],
    1, [Rank by Hotel],
    2, [Rank by Agency]   
)

Use the correct measure for each parameter order field value. Use the parameter field and  the measure  above in your visual.

Please see attached sample pbix

Note: Ignore the other pages.