Hi Barry,
I'm not sure how you get 15 overlaps. With four circles it seems to me that you only have 11 combinations of overlaps: 1-2, 1-3, 1-4, 2-3, 2-4, 3-4, 1-2-3, 2-3-4, 1-3-4, 1-2-4, 1-2-3-4. Am I missing something? Or are you including the individual circles as if they were combinations, which would give 15 "combinations".
Also, do your data values correspond to the areas that you want in the various combinations? If so I believe you could use Solver to solve all the conditions simultaneously to find the positions of the four circles that would satisfy all the overlap areas, basically solving for the x,y coordinates of each circle centerpoint and the radius of each circle. Once you have these data values, drawing the circles using Shapes should be fairly straightforward. I would recommend filling them with different semi-transparent colors so that the overlapping areas show up in different colors.
Damon