EDIT: I\'ve updated the example code and provided complete table and view implementations for reference, but the essential question remains unchanged.
You could always go the CROSS APPLY way.
ALTER VIEW [dbo].[ViewOnBaseTable]
AS
SELECT
PrimaryKeyCol,
ForeignKeyCol,
ForeignKeyRank,
DataCol
FROM (
SELECT DISTINCT
ForeignKeyCol
FROM dbo.BaseTable
) AS Src
CROSS APPLY (
SELECT
PrimaryKeyCol,
DENSE_RANK() OVER (ORDER BY PrimaryKeyCol) AS ForeignKeyRank,
DataCol
FROM dbo.BaseTable AS B
WHERE B.ForeignKeyCol = Src.ForeignKeyCol
) AS X