On him [Peter] he builds the Church, and to him he gives the command to feed the sheep [John 21:17], and although he assigns a like power to all the apostles, yet he founded a single chair [cathedra], and he established by his own authority a source and an intrinsic reason for that unity. Indeed, the others were also what Peter was [i.e., apostles], but a primacy is given to Peter, whereby it is made clear that there is but one Church and one chair. So too, all [the apostles] are shepherds, and the flock is shown to be one, fed by all the apostles in single-minded accord. If someone does not hold fast to this unity of Peter, can he imagine that he still holds the faith? If he [should] desert the chair of Peter upon whom the Church was built, can he still be confident that he is in the Church?" (The Unity of the Catholic Church 4; 1st edition [A.D. 251]).
He's clearly not talking about the chair of Peter as something that pertained to all of the bishops.
In his letter to Pope Cornelius, he writes:
After such things as these, moreover, they still dare-a false bishop having been appointed for them by, heretics-to set sail and to bear letters from schismatic and profane persons to the throne of Peter, and to the chief church whence priestly unity takes its source;51 and not to consider that these were the Romans whose faith was praised in the preaching of the apostle, to whom faithlessness could have no access.52
Still think that Cyprian's cathedra Petri has nothing to do with Rome?
It's amazing to me how some Protestants, who proudly claim that they let no man interpret the Bible for them, run after interpretations of the Fathers written by men, although the primary sources are there for everyone to read.
According to catholicfundamentalism.com if you have three Baptists in a room, there are at least two separate churches represented and a third about to start. Actually, the Baptists are closer to the truth if they are Fundamentalists than are most left-wing Catholics. catholicfundamentalism.com brings it all together, but I warn you, it's like kicking the tar baby. Weirdest website out there.
Good work, you saved me some searching!
Well, Cyprian, the answer seems to be yes, one can imagine such a thing.