Hard to even approach answering this question without some kind of workable definition of "objective" and "universal" and "morality." What does a person mean when they say all these words together? My best guess would be something like, "All people would agree that any action recommended by this morality are right, and any action prohibited by this morality are wrong, and this morality either recommends or prohibits…
Even so, a moral framework doesn't have to be complete to be justifiably considered "objective", so attempting to find universally acceptable moral axioms may not be altogether futile.