We said that the problem of ethical relativism disappeared if there was no fundamental disagreement. But is that really true?

Suppose there is fundamental agreement on ethical principles, but still no objective basis for the principles? We can still imagine someone putting forward a different set of moral principles. And we can still imagine asking whether there is a way to prove one and only one set of principles to be true or binding. Wouldn't that bring out our basic problem in spite of the fact that there happens to be fundamental agreement on principles?

It seems to me that the fact of fundamental agreement eliminates conflict here and now but doesn't resolve the basic philosophical problem.