|P is for Practical|
I hope I'm understanding the problem. Regardless, it was an interesting puzzle (and a great question).
I understand you to be saying that you want all possible merges of the combinations of set A with the combinations of set B. And I think that by mentioning the potential for overlap you're saying that any merge that would result in an overlap should be disqualified. I don't think it is sufficient to just generate all combinations of set A, and all combinations of set B, merge, and shuffle. That would not result in a result set of all possible non-overlapping merges.
My solution creates all possible combinations of set A (3 at a time), and then iterates over that list in an outer loop while merging all possible combinations of set B (taken 2 at a time) that don't result in an overlap of any elements. The implementation sacrifices speed efficiency in favor of memory efficiency; we never actually hold onto any full list of combinations of either set A or set B. We just use the iterators for each set. That means that the set B combination object will be created and destroyed on every iteration from set A.
Here's the code:
If overlaps between set A and set B are permitted, delete these three lines:
...and if I totally missed the boat I'm anxious to see a correct interpretation and the resulting solution code! :)
Update: In the update to your original post, and further clarified in a message to me, I see that you may be needing to merge multiple sets of combinations (ie, more than just two). I don't see any solution that doesn't involve diving deeper and deeper into nested loops, driving your big-O complexity higher with each additional set of combinations.
Is this just one way of approaching a more general problem that you're trying to solve?