It's still possible to use decision theory and an utilitarian framework (and/or bounded rationality) to unify whatever two random people's morals happen to be. Sure, in theory people with infinite time on their hands will come to agreement about everything - Aumann's agreement theorem. But even if they don't, it doesn't matter, as they are still going to maximite their utility as best as they every point in time can, with all the complexities involved due to our neurobiology and path-dependence on personal experiences.
Now, that said, ignoring pathological cases (both abstract/hypothetical and real clinical - eg someone just on the verge of suicide) rational agents have instrumental goals, such as survival, gathering resources to be able to survive, keeping warm, but not too warm, etc. And this is where "the fun begins", or the complications. Because there are many possible strategies, just putting them on a predatory-cooperatory spectrum gives a sort of handle on them. (Obviously there are situations where otherwise even the most cooperative-minded person can end up selfish, and vice versa.)
And abstracting all this basically gets you Rawls' Theory of Justice, which says, that since you don't know what situations you can end up in (eg. you don't know if you get cancer in the next year or not), you should think through many situations and determine what would you prefer in them, and then try to find moral norms that are the most satisfiying in the most cases. (Eg. the most fair rules.)
Of course this is extremely handwavy, and naturally - as things in philosophy are rarely - the matter is not settled, but I think there there is a convincing argument to say that sentient minds can find a common moral ground, if they want to.