I want to argue that the rule of law is one moral system that applies to all organizations. Sure, some overstep and may gain some advantage due to that. But in principle and hopefully on average the result should be net negative. In democratic countries the laws are more or less directly the will of the people, about as egalitarian as we can get, no? Anyways, following the rule of laws should lead to “morally sound” corporations as defined by the people. Corporations can go further than what is legally required, too. That is often used in marketing.
Finally i think the same principles apply wherever humans (or other species) compete. Humans on the whole are not entirely cruel barbarians, we try to care for individuals who are not able to care for themselves etc. Whether “true” altruism exists is another discussion, but it certainly looks like it. So if that’s how people act, why should corporations be more corrupt than the bodies that make them up and govern them?