Algorithm to create "Spot It"/"Dobble" cards, but with two common images from any two cards

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In the ordinary "Spot It"/"Dobble" game, there is exactly one common image between any two cards. At the moment I am trying to modify the algorithms already available on the internet so that any two cards have two, three, etc. elements in common.

Unfortunately, I have failed and am now looking for ideas on how such an algorithm could look in concrete terms. Do you have any ideas for such an algorithm? enter image description here

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