Make Cell Blank if all Columns are "N"

Try this. I combined with your other formula so it will check if all = N first and if not, it'll run through what you previously wrote. I also updated for @row to speed it up.

=IF(AND([PAR Items]@row= "N", Proxies@row = "N", Commissions@row = "N", Constraints@row = "N", [APX Reports]@row= "N", [MRFP/SMA]@row= "N", Commentary@row = "N", Attachment@row = "N"), " ", IF(OR([PAR Items]@row= "Y", Proxies@row = "Y", Commissions@row = "Y", Constraints@row = "Y", [APX Reports]@row= "Y", [MRFP/SMA]@row= "Y", Commentary@row = "Y", Attachment@row = "Y", (COUNTIF([PAR Items]@row:Attachment@row, "") > 0)), "Incomplete", "Complete")

Ok. That makes sense. The first thing to establish is how many possible entries there are. If there is the need for flexibility to allow for a differing number of columns whether you plan to add or remove, we can use a simple COUNTIFS across the range.

=COUNTIFS([PAR Items]@row:Attachment@row, OR(ISBLANK(@cell), NOT(ISBLANK(@cell))))

As long as [PAR Items] is the leftmost column and Attachments is the rightmost column, you can add, remove, or rearrange everything in the middle.

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For the sake of this example though, I will use a hard coded number. Your screenshot shows 8 columns within the range, so I will use the number 8. If you need the flexibility of the COUNTIFS, just replace the number 8 with that formula within the overall formula.

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So we will start with "Y". If any cell within the range contains a "Y", we want it to display "Incomplete".

=IF(CONTAINS("Y", [PAR Items]@row:Attachment@row), "Incomplete", 

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Next we will say that if they are ALL "N", display a blank.

=IF(CONTAINS("Y", [PAR Items]@row:Attachment@row), "Incomplete", IF(COUNTIFS([PAR Items]@row:Attachment@row, "N") = 8, "", 

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If there are zero cells with a "Y" in them making the first argument false, and not all cells contain an "N" making the second IF statement false, then the only other option would be to register it as "Complete" and close out the formula.

=IF(CONTAINS("Y", [PAR Items]@row:Attachment@row), "Incomplete", IF(COUNTIFS([PAR Items]@row:Attachment@row, "N") = 8, "", "Complete"))

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And there you have it. Short, sweet, and to the point.