Prema does not live uncovered litter boxes, she loves some privacy. Maya is the same but will use it uncovered when I just finished cleaning it and I've had no chance yet to put the lid back on. Foxy has only used covered ones. We have 2, one we always keep on the balcony and when it gets hot the second we keep the second one there as well.

I've actually heard that each cat should have it's own litterbox.
I'm not sure that it would work. My sister lived with me for a while and we had 5 in cats sharing, we had a few litter boxes, and they all used only 2 of them. Obviously they expected us to clean them several times a day