Union grouping in bipartite graphs?
Have you heard about the intersection graph? You can try to draw players as points, connections (team mates) as edges and teams as transparent coloured blobs on top.

As for your original question, I cannot understand your goal. I think your formulation is not well defined / incomplete. Suppose you have teams A [1,2] B [2,3] and C [1,3]. What do you want to display? Do you want to list the parts of the Venn diagram? I think that for more than 3 sets this can become more cumbersome than the bipartite graph itself = simple listing of team compositions.