I know about 6 tunes for "While Shepherds watched" well enough to sing from cold, around 20 more I can when reminded of them and there's perhaps another 20 I've heard once or twice that I would need to actively learn to the tune for.

Last weekend I was told by a West Gallery leader of 156, but I'm not sure if that means he actually has 156, or 156 he knows of. He also said that the tune commonly used (Winchester Old) was picked specifically because it was not used by any locality.