Can Papal Supremacy be relinquished? Is there anything in the Roman Catholic doctrine of papal supremacy that would prohibit the Pope from relinquishing his authority as head of the Church, and instead be "First among Equals?"

One of the fundamental differences separating the Roman Catholic Church from our fellow Christians in the Orthodox Church is the issue of papal supremacy. Rome believes that the Pope is the leader of the entire church, while the Orthodox believe that the Bishop of Rome is first among equals.

Given the pressure of secularism (both from outside and inside the Church), I believe that it is high time for us Christians who believe in the ancient faith to be united.  

My questions is this: Given the Roman Catholic doctrine of papal supremacy, would it be possible, for the sake of Christian unity, for the Pope to relinquish that supremacy and become first among equals? Could he decide that it would be better for the universal church if he acted as "Prime Minister" of the faith, instead of "King of the faith?"
Papal primacy belongs to the very nature of the Church. No one can change how Christ Himself constituted His Church.

The First Vatican Council defined (Pastor Æternus ch. 2) the dogma that there will be a perpetual line of successors of St. Peter, the first pope, with "Primacy over the universal Church":


  If, then, any should deny…that blessed Peter should have a perpetual line of successors in the Primacy over the universal Church…: let him be anathema.Si quis ergo dixerit, non esse … ut beatus Petrus in primatu super universam Ecclesiam habeat perpetuos successores…: anathema sit.


(taken from my answer here)

Thus primacy is also perpetual.