If we use king Neb's statue as one of our guides, we can see that there are four manifestations of the 4th Beast, each at different stages of its evolution..
1. Symbolized as Iron- the Roman Republic.
2. Divided being Two legs of Iron-.Roman Empire, both East (Byzantine) and West (Roman Catholic).
3. Two feet of Iron mixed with clay- Independant Europe.
4. Ten toes of Iron and clay- European Union.
Hold on there, you are looking at the statue with a preconceived theory as to its identity, as being a "manifestation" of the 4th beast. You are looking at the 4 th beast and going back into the statue in order to justify a wrong conclusion. I suggest you simply take scripture as it reads, and Daniel's interpretation as he relays it to the king.
4 empires. The head of gold, Babylon. 3 more to come, each with waning moral value but increasing tyrannical power. The 4th Empire, as history revealed and with which you agree, is Rome. Later as you noted, it changed in character, and became associated (not completely united because iron doesn't mix with clay) through politics and shared policy. The clay can be understood, by studying scripture and how it is defined elsewhere, as representing God's people. I'm OT times, God people was Israel. But we aren't talking about OT by the time the iron becomes mixed with clay. Rome never made any political agreement with Israel that could even remotely be worthwhile God's gift of the dream to the world. And note also that the destruction of the ten toes introduces a time where those powers have become utterly ended, their influence over, and a new order, the kingdom of God, in its rightful position. So the clay must apply to the church. In the beginning, the clay was malleable and able to be worked according to the designs of the Master Potter. But not so by the time the clay became entangled in politics. This was the 4th century, with the beginnings of the rise of papal Rome. A power that has totally depended on politics in order to sustain its influence in the world, and has this become miry clay, and unworkable in its present condition.
So that's all we can deduce from a study of the iron portion of the statue, and an intelligent and informed study of history.
To add more information, we then must go to Daniel 7, and against as you rightly pointed out, the 4 th beast. We need to take one step at a time, and not presume we know more than has been revealed. While I agree that pagan Rome divided into two branches, I do not believe that we should relate that back into the prophecy. Then we would need to account for 5 toes in each branch. We would need to account for the papacy's influence in both. While there was some important political moves made by the eastern Emperor Justinian towards establishing the papacy as a legal power with authority, by that time the western branch had dissolved. Reconciling that with the statue cannot be done. Hence we look to the 4th beast, and see if their are historical correlations there confirming what we have thus far found, and such needful confirmation we do indeed find, and a lot of it.
We must consider first the ten horns, powers or nations that arose from the head of the beast. Remember, one step at a time. No presumptions, no guesswork, no taking present day conclusions and attempting to fit them into ancient prophecy. We take the prophecy first, and use that as the basis for understanding history. The statue formed the framework. Note we are adding the sinew and tissue. There must first be an answer to an obvious question. What area is under scrutiny in this picture? All prophecy deals explicitly with the major impact made upon God's people over the course of history. That's why we don't find South America, China, or Australia in prophecy. Though there was important events and Christian influence in this nations, as far as the prophecy is concerned, we need to focus more on what affected Israel as a local literal nation, and then later, how the church developed into a global spiritual power. We see that particularly in Revelation, but we aren't there yet, although there are hints off that in Daniel.
The ten horns became 7. As the Empire was dissolving, what took place in Europe, (the principle concentration of Christian activity in the first centuries of the new millennia) that powerfully impacted the Christian community? What we find its that through power Spirit filled evangelism, the nations that invaded the former Empire as Rome abandoned it, were all converted to one form of faith or another. All of them were formerly pagan entities, but through the influence of evangelists such as Wulfilas, Patrick, and earlier word of mouth arising from the ministry of Paul particularly in Galatia, the gospel spread very quickly from Asia to Britain before the turn of the first century, and it was from Irish evangelists such as Columba and Columbanus that central Europe, specifically Germany and France and Switzerland, became converted. Of course, those nations didn't exist as such several centuries later, with the influx on Germanic tribes with the dissolution of the Empire in the 5th century.
We find at least 10 explicit criteria confirming the papacy as there little horn. That little horn, which arose to power through accidental circumstances and through the help of Justinian, became an opposing enemy to the evangelism previously mentioned. And throughout history, there have been two main branches of Christian thought and policy that dominated Europe. The politically powerful papal Catholic church that inherited the throne and authority of the Caesars, and the evangelical churches that inherited the gospel from the apostles. Those two branches have been in tension ever since.
This the prophecy of Daniel 7 finds is complete fulfilment in the rise of that little horn, which had power over the Saints, and made war with them. In later centuries, as Revelation's prophecies unfolded, we see a global conflict ongoing between those same powers, one represented by the harlot, the other by the pure church of Revelation 12, and in chapter 13 we see them sea beast still comprising those powers even from Daniel 2 and 7 inheriting their pagan traditions and practising them under a counterfeit Christian guise.
