I think in order for the 5 official solutions for two circles to be valid, by definition each circle must be of a different radius. Therefore, each additional circle must also be of a different radius:
[1", 2", 3", ...]
I fear that not even that would be sufficient to allow for all possible configurations down the line. Have a look at some of the images starting at around 4:10 of the following video.
(Spoiler alert: the following YouTube video talks about a very similar problem, just with touching circles disallowed)
Even with just four circles, it is apparently necessary to draw one circle bigger than the whole page, while another one is tiny. The expert in the video calls these configurations "delicate", but I look at them and have to assume that something is wrong with the original problem itself if it leads to random solutions like these. It's just not beautiful enough for my taste. :)
Duplicates. Am I wrong in thinking that each setup or scenario would have one less number of variations than the previous setup? Due to duplicates.
Can you clarify what exactly you mean by the term "setup"? Is it the same what I called a configuration, or is it something different?
By the way, it's fun to see that this conversation has quickly led to a point where we need to define strict terminology. :D