Does love lessen with more partners? Not necessarily. Sometimes the opposite happens!
However, it is true that there are only so many days in the week, hours in the day, etc.... Time is limited, and very busy people almost certainly cannot manage several (or many) "romantic" relationships simultaniously.
There are so many variables in this question. Love itself doesn't divide, like pie does. But time does -- and there's no getting away from that. But some people are okay with only a few hours a week, while others really do need a lot more together time with each of their partners.