grammatical number - plural possessive form of a mutated plural?

Here are two examples of mutated plurals:
more than one goose= geese;
more than one man= men

1)Say you had 2 or more groups of geese. I.e. group #1= African geese & group #2=buff geese. If you wanted to associate these groups together but still observe the fact that they are different types of geese, would you say geeses? (Buff geese + African geese = geeses)
Taking this one step further, if these two distinct groups of geese share in the possession of something, would geeses' be correct? Say, one type of illness is common to two sorts of geese. [illness common to Buff geese(=Buff geese's illness) + the same illness is common to African geese(=African geese's illness) --> geeses' illness? ]

2)Say you had 2 or more groups of men: men from France(Frenchmen), men from England (Englishmen), and men from Ireland (Irishmen). Let's say you want to refer to the "European charm" that these groups of men have in common while still noting that there ARE different and distinct groups of men involved(i.e. different people groups--> peoples). Would you say the mens' charm?

I guess I'm just curious if you can make the sum of multiple groups possessive while keeping a distinction between these groups intact.
(distinct GROUPS with similar possession)