There is one way to harm your fish with too much filtration: If the fish aren't made to deal with high currents (bettas are a good example of such a fish). With enough filters, you could probably turn your aquarium into a veritable whirlpool, which would be detrimental to your fishes' health.
Three, however, isn't all that horrible.
As was said above, there's little benefit. Once you've reached the threshold of the
ammonia being more or less instantly converted to nitrites and the nitrites being more or less instantly converted to nitrates, they provide very little advantage.
However, if one of your filters crashes, or if you need to cycle another tank, the extra filters will be helpful.