Say I have a non-unique, non-clustered index with some included columns. It covers a bunch of frequently used queries. I could make it an unique index if I add another column to the index, assuming unique indexes are better than non-unique ones.
If it's just so that you can make the index unique, I probably wouldn't bother.
And, what if that column also happens to be part of the clustered index for that the underlying table? Would that alter your recommendation?
No, not really. If the index unique you should mark it as unique, don't go adding columns just to make it unique unless it also lets more queries use the index or otherwise enhances performance of something.
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