In a single sheet wanting to copy D3:N if either B3:B or C3:C = S2. I'm sure there is a simple formula to do this I am just unable to find it!
Try a formula like the following:
Since FILTER conditions are treated as ANDs, using in your two conditions directly would only let rows through if B3:B AND C3:C matched S2. Instead I use a plus sign to add TRUEs and FALSEs since that works as the Boolean OR we need.