"And is, then, all which is just pious? or, is that which is pious all just,
but that which is just, only in part and not all, pious?"
Socrates - Euthyphro
It is obvious in the responses by Socrates in the Euthyphro that some form of universal piety supersedes the plurality of gods and human opinion.
This is the point of the search for understanding Piety in the dialogue. Many responses to these types of questions in philosophy result in a neutral position. In other words, the cyclical nature of the Euthyphro dilemma causes too many to respond with a neutral response.
But Plato does not accept a neutral answer to the question of God in philosophy. What is obvious in the history of philosophical thought is that questions surrounding God matter. Does God exist? What is the role of God in morality? What is the role of God in social issues?, etc.
Questions involving God cannot be avoided. Thus in philosophy we must explore these questions with honesty and humility. To blatantly stop all dialogue about God and philosophy results in no philosophy at all. Socrates would have never accepted avoidance of the questions surrounding God.
Whereas Euthyphro stopped all discussions about the role of the gods in defining piety by declaring that all that the gods demand must be obeyed, blindly if necessary; Socrates pushed for a logical understanding of all things pertaining to the gods, or even God. If the plurality of gods resulted in conflicting application of morality, then Socrates concludes that there must be a greater Form of piety that transcends all mimicked, or copied attempts of pious action.
For Socrates, the true definition of piety involved the true form of piety that transcended all discussions of religious dogma. To avoid these discussions out of a position of agnosticism would also be a violation of true philosophical exploration.
So what is Piety?
For Socrates, piety is the honest and pure action which is right despite what gods might insist. This is not because the gods have no role in defining piety, but rather that human attempts to impose pious action in the name of the gods were too often flawed copies of the purest piety. Thus, piety must be in its purest form an idea that is beyond human efforts to make. This answer does not grant permission to dismiss attempts to be pious. But rather inspires all pious action to be greater than any human effort. Perhaps a God that transcends all gods is what Socrates searched for. Perhaps true Piety exists beyond all religious dogma. Regardless, Socrates observed through philosophy that genuine piety involves God since true piety is misinterpreted by pious religious people like Euthyphro.