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In QGIS, I have a polygon layer in which every polygon intersects at least another one.

How do I select the ones that intersect more than two of them?

Using overlay_intersects(@layer) selects all of them.

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You can use overlay_intersects with the expression 1 to return a one for each intersecting polygon, then sum and select sum over 1:

array_sum(overlay_intersects(layer:='yourlayernamehere', expression:=1)) > 1

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