Well, so, can I say that if the noun/object is singular for each one, then, I can use the singular in this situation? Such as, many people's body, many people's heart, many people's nose.
Oh, and, if the noun is singular or plural, then I can use the singular or plural, right? Such as many people's pens, many people's shoes??
This is one of the most difficult questions you can ask. I remember asking it a couple of times too, and I never got any clear answer.
You might be interested in this too, it's an old thread of mine:
If I had to think of an explanation, I'd say that probably it all depends on what you focus on. That's usually the explanation in a lot of similar cases, like notional agreemen