Go back to Conditional Formatting and delete any prior rules you have created for this purpose, then (full columns A:H selected) create a new rule using the option to Use a formula to determine which cells to format. Supply the following to the Format values where this formula is true textbox:
You likened your requirement to the existing Format only unique or duplicate items options so I assumed that you wanted both the first and any subsequent duplicates highlighted.
Caveat: If you have more than ~1000 rows then you may experience some latent calculation lag. This could be reduced with a helper column holding a concatenated value as mentioned in the previous reply. Which method you choose will depend upon the number of row within the conditional formatting rule's Applies to: region and what you feel you can live with.