I have made camp for one or more nights in a pristine wilderness. It may be desert, tundra, or a forested environment. At a suitable distance from camp, I have dug a nice cathole (toilet-hole) and done my business. Now it's time to sleep. Should I close my cathole and dig a new one tomorrow, or do I leave open and reuse my cathole and wait until I depart before closing it? Maybe an open cathole is more likely to attract animals, but multiple catholes leave more traces than just one.
I follow the idea of leaving as less a trace as possible. So what I do is to reuse the cathole. The problem with multiple catholes is how much damage it does to the landscape (especially if the ground is covered with grass).
And anyway, it goes without saying that once you are done with your business you'll put some soil into the cathole to reduce the smell and thereby reduce the possibility of animals getting attracted :).
The solution to this and especially when you have multiple people in a group and so want to limit the number of holes, is to use a single hand width trench instead individual catholes.
You start by making one cathole that is wider than long, and as it is used, you fill in and the dig to one one side using the diggings to cover up as needed. When you move on, you completely fill it in.
It should be no wider than a normal cathole and my understanding is that this is Forest Service's preferred method for larger groups instead of everyone digging individual catholes.
Based on Rickeyship's feedback, I'm changing my answer.
The answer depends on your environment, so try to find out what makes sense in the context of where you'll be. My original answer works well in the woods of Missouri where your droppings will be subsumed into the environment, and you can make your catholes undetectable. However, if you're in a fragile environment, or an environment where droppings take longer to process, that approach would be problematic. Ricketyship gives the case of the western ghats as one such example. The arctic might be another, if I were to guess.
In the fragile environments, follow his advice of a single, larger cathole.
But overall, I think the right approach is to know the environment you're entering, and determine what the right answer would be in that particular context.
Your cathole shouldn't leave a trace - that is, shouldn't be visible to anyone after use. So in that regard, maybe work on making your covered catholes invisible.
When I use them, and when I've read about them, they're always small and only big enough for one use.
Properly made, closed catholes shouldn't attract animals. Open ones might, but I've never left a used one open. One thing I've done that was helpful was to dig one before gong to bed so that I can use it first thing in the morning without need time to locate and dig one.
Also, a cathole shouldn't damage the environment. So, save the top layer, whether grass or sticks and leaves, and put it back. Your droppings and toilet paper are fertilizer, and will become part of the earth quickly, benefitting the environment.
Knowing roughly how many times it will be used, it should be deep enough for at least that. After each use, foliage and earth should be put in to cover5 faeces. At this point, since it's covered effectively, forget it until the last time it's used, then fill it properly so it looks like nothing happened.