I have a pool of 15,000 unique* items. From that set, there are roughly 3200 sets of 60 items, selected non-randomly (in fact, for the sake of the framing of the question, let's say that each item is intentionally chosen for a specific reason). I have the list of all items that are in at least one set; said list is about 5500 items long, and also includes the total number of sets each item is in. The most popular item is in roughly 60% of the sets, and the list goes all the way down to items that only appear in 1 set.
Additionally, there are similarities that exist between the different sets that manifest themselves in the form of tendencies. For instance (with random values given), 30% of the sets are similar according to one "tendency group", and tend to include items #1, #50, #2006, etc. more often than other tendency groups; 20% might be similar to each other in a different way, and tend to include items #65, #700, #5000, etc. more often than other tendency groups. Thus, there's not exactly one set of "expected values" (which would make this question similar to this one), but rather upwards of a dozen groups of "somewhat similar values." I looked also at this question, but, as someone with a limited grasp of the subject, it doesn't seem like it's exactly what I'm looking for.
How do I compare each set to each other in such a way that I'm able to compare each item from a given set and see how it compares to other items that appear in similar sets?
Specifically, if given a specific set, if I were to replace one item, which item would I take out, and what would I replace it with, to make the set more similar (less unique) compared to other sets. Extra points if the method is capable of making the set more similar to one specific (or perhaps simply being selective towards one) tendency group (or more).
In typing out this question, I've become aware of the Jaccard index, but that seems like it's more suited for comparing two sets of data to each other, not looking at an individual item across multiple sets and looking for similarities in that respect, but I could very much be wrong.
*I say unique; even though they may differ in one aspect, some items functionally or even have exactly the same characteristics except for their name, but I'm not sure how much that matters.
Edit1: the unique items are Magic: the Gathering cards, and the sets represent individual decks. Does that help?
Edit2: Since posting this question, I have become aware of the existence of "market basket" analysis, but, as a laymen in this field, I have no idea where to even begin to conduct said analysis.