I am wondering if the Priest offers Mass in "Persona Christi," wouldn't there be Many "Christs" in a concelebrated Mass? It seems that way to me. Why aren't the laws that there is just one Catholic Priest at a time?
"Unless the benefit of Christ's faithful requires or suggests otherwise, priests may concelebrate the Eucharist; they are, however, fully entitled to celebrate the Eucharist individually, but not while a celebration is taking place in the same church or oratory."
Shared "presidency" at a Mass was actually the norm in the early Church. There is substantial evidence that in the 2nd and 3rd century, it was customery for the Bishop to be the principal celebrant surrounded by his priests on either side. Concelebration was the regular course until the middle-ages when the practice of private Masses began to become more the norm. By the 12th century, it was usual that only at ordinations that the newly ordained would concelebrate.
More regular concelebration has been restored to the Church since Vatican Council II.