JulianF, are you using this visualization to tell a story? explore? display causality?
You say that they can have up to 6 comorbidites (poor souls). I have a suggestion...
a******
ab*****
abc****
abcd***
abcde**
abcdef*
abcdefg
because you have set of 6 with the possible combinations (7 if you count no comorbidities, but I don't think that is where you are headed with this), there will be overlapping i.e. 6 with 2 and 3 (OR 2 with 6 and 3)
Here's the hopefully elegant part of my suggestion. Let column a be 'diabetes', use very small color coded boxes to highlight a unit, make a line within the bar to segment and create a 1st part of column 'a' which will be just 'a'. Pick a 2nd comordities say b = 'heart disease' mark boxes by color that are similar to column b, continue ab, ac, ad, ae, af, ag as the set of all a with one other comorbidities. If each is one unit and a marker segments column a after a+1 other, then you have an area that highlights diabetes plus one other. Additionally, looking with in this area gives you a quick visual glance of what diabetes hangs out with. Repeat this process on up for a with 2, awith 3 up to 6.
Do the same for b, but remove ba (the * at the top).
There is a name for this kind of graph. I've seen it like twice, both times it was interactive and... beautiful. I don't know where I saw them or what software they used or the name of this kind of segmented bar graph.
The graph could additionally modified where the x-axis is number of comorbidites, so column a would be 1 comorbidity with 6 segments and g column being the 6 comorbid. I have a gut feeling this turn ugly, but just a feeling...
Just an idea
Darin