In this article, I will argue that it is time to rethink and reconfigure some of the established assumptions underlying our conception of moral responsibility. Specifically, there is a mismatch between the individualism of our common sense morality and the imperative for collaborative responses to global problems in what I will call the "collective age." This must have an impact also on the way we think about the responsibility of corporations. I will argue that most plausibly we ought to reframe corporate responsibility as a conception of collaborative responsibility. Such a conception of collaborative responsibility is characterized by five key elements: first, it is based on the moral imperative for collaboration. Second, it shifts emphasis from commission to omission. Third, it is not only negative but also, and perhaps essentially, positive responsibility. Fourth, it is political responsibility. And finally, it is, most basically, human rights responsibility.