Supererogatory actions are things that would be good to do but aren't morally required. In some sense, there are lots of good things that I could do that aren't morally required. I can't do every possible good deed I could do, for instance, because I only have a limited amount of time. But the difference with supererogatory acts is that they're supposed to be above and beyond the call of duty. They're actions that would be wonderful to do but are not required in the sense that I would be a better person if I did it, and the action is better than what I end up doing instead, but I still have no obligation to do it.
I've argued that Christians should not accept the category of supererogatory acts. I'm not changing my position on that, at least when it comes to human actions. I don't think there are any cases where I'd be doing a better thing if I did something different but am nonetheless perfectly ok not to do it. If I'm doing something less good, I'm failing in my responsibility to be perfect as God is perfect. I don't see how Christians can accept biblical teaching on ethics and accept this category for human action.
What hadn't occurred to me when I wrote the aforementioned post was to ask about whether certain actions are supererogatory for God. I think the standard Christian view has been that some things God actually does are supererogatory. It's hard to see grace as anything but supererogatory. It's undeserved favor, and how can God be morally required to bestow undeserved favor? I'm not going to question that line of reasoning, so I think it's fair to say that I need to revise my view. I'm not denying that any actions are supererogatory in general. It's just that human beings ought to do the best action in any circumstance.
One way to get such a result pretty easily is to take a page from Immanuel Kant, who speaks of a divine lawgiver as the sort of being who would have no obligations to begin with. His argument is that it doesn't make any sense to think of God as having obligations, because obligations make sense only if the being with the obligations could possibly fail to do the things the obligations require them to do. (William Alston interestingly applies the same line of thought to beliefs. God directly knows every truth, and therefore he must not have beliefs, because beliefs imply that the beliefs could be false, just as obligations imply that you could fail to fulfill them.) If Kant is right, then God is never obligated to do anything, and so every action God performs is supererogatory, but it still might make sense to say that no human act is supererogatory.
But I don't think that explanation is sufficient. I want to say that some things God does necessarily result from his moral perfection, and other things are a gift that his nature doesn't make him do. I want to say that he didn't need to create and would have been perfectly good had he not created. I don't want to say God is morally better for creating, and I don't want to say God is morally better for choosing to save people from the eternal destruction we all deserve. But even if all that is true, it seems that there are some things that are inconsistent with God's nature, such as making a promise and not keeping it or allowing the universe to be intrinsically bad overall. That means that something the concept of supererogation was supposed to capture is true of God in a way that it's not true of humans, and it doesn't just result from God's having no obligations.
I think the difference has to lie in some explanation why it isn't better for God to do this thing that seems like it would result in a better world, whereas it is better for me to do things that would lead to better consequences. That difference has to lie in God's nature. God would be perfectly good without even creating, so it doesn't make God's character or nature better to create. Also, God is infinitely good, so it doesn't make the totality of things better if God creates things and doesn't just exist on his own. On the other hand, I am imperfect, and there are always ways to be better. I have an obligation to seek to be better unless I am perfect. That seems to me to be the real reason why it isn't even better for God to do better things, while it's any merely human being's obligation to do the best thing possible.