When adding finite sized, circular, randomly placed holes on a finite area the number of holes increases with each addition.
After a number of circular holes have been added, adding another makes the new hole and an existing hole merge and the total number of apertures in the area does not increase.
When more circular holes are added, the new circular hole joins empty regions and the total number of holes decreases.
How does of number of circular holes added relate to number of holes in the sheet?
Adding a few holes makes a sheet a fish net but then adding more holes destroys the net.
Nine circular holes have been made in the blue area resulting in six holes.
While it looks like a relatively simple question, it's one that doesn't have a particularly simple answer. In fact, the simplest answer I can offer is that there is an entire sub-branch of mathematics looking at this and related problems, called percolation theory.
Probably the most interesting part of it is that depending on the distribution you're using to place the holes, there is usually a critical point where you suddenly transition from "holes can go anywhere and not interfere" to "the space is filled with holes and if you add another one then the area that isn't holes is pretty much guaranteed to fracture into many parts".