The twins, Romulus and Remus, were added in the Renaissance, but the date of the creation of the She-Wolf has been the subject of debate for a century or so. I discussed some of the early Medieval sources describing the statue outside the Lateran Palace, as well as a drawing of it standing there in the Renaissance, in this post (scroll down):
In addition to the evidence I included there, I should add one key piece of very early Medieval evidence. When Charlemagne (crowned Holy Roman Emperor in AD 800) built his capital at Aachen, he went out of his way to make it the New Rome of his new Roman Empire. This included building a magnificent palace from which to rule it, modelled on the pope's palace in Rome; Charlemagne not only named his new palace the Lateran, but also arranged for an ancient statue of a She-Wolf found in Gaul to be brought to stand outside the palace, just as one stood outside the Roman Lateran. It is possible that a different She-Wolf stood outside the Medieval Lateran palace from the one now on the Capitoline, but unlikely.
The problem is that ... if the Capitoline She-Wolf is a post-Antique creation, one must ask who was able to create such a statue? La Regina's objection seems to be that the statue was cast whole, but there is no evidence of Medieval bronzes cast whole of this size and quality.
Previous claims have tried to date the creation of the She-Wolf to the time before the sources place her outside the Lateran Palace, meaning that she must be a Carolingian work. The problem with this, is that one must wonder why such emphasis was placed in Carolingian sources on Charlemagne's re-creation of the Lateran with a Lupercalia outside, if there was no Lupercalia outside the Roman palace he was imitating. And there is no evidence for anyone having the ability of cast such a piece at the time, and the nearest comprable work would be the great German Lion a couple of centuries later.
The only new suggestion I am seeing in the press coverage is that it was copied off a statue brought from Constantinople in 1204. Again, I would question whether the ability to cast such large pieces whole existed in 1200s Rome, and why there are no other examples of similar style in Medieval sculpture as comparanda.
Although many bronzes were brought back from Constantinople after the capture of the city in 1204, and we know that there was a Roman Lupercalia in the Hippodrome in Constantinople which seems to have survived to the time of the Fourth Crusade ... The Capitoline Lupercalia seems to have been outside the Lateran Palace in Rome before then.