I know they can run on 2, Im wondering if I could connect three to each miner or will it only work in arrangements of 2 or 4?
You could run on 3, but the load won't balanced across the 2 cards - one card will only have 1 cable powering it and that cable will have the highest risk of melting.
You could buy PCI-e splitters and run 3x PCI-e cables (2 + 1-into-2) per S3 miner. That way you can balance out the odd cable across the 2 cards.