All of Europe by 1700 AD

So the idea is some empire or Royal line unifies the European continent. We are defining Europe as the the Urals to Ireland. From Sicily to Norway and from Norway to the gulf of Gibraltar and from Gibraltar to the the Caucasus mountains.

The state is allowed to have as much colonial territory or holdings in the Middle East/North Africa or Anatolia as you want.

Make it happen or explain why it can't.
 
The House of Habsburg Lorraine unites Europe by marriage and conquest.
Philip the Handsome/Fair lives longer/no German protestants
Ferdinand only King of Hungary
Philip II becomes Emperor of HRE
No Dutch Revolt
England and Spain/HRE united after marriage
French wars of religion the Valois and Boubons lines extinct The powerless Courtenay's becomes powerless Kings
The Habsburgs elected as Kings of Poland/Lithuania
Habsburg March to Moscow in the Time of Troubles
There is still Scandinavia the Balkan and Anatolia and the Caucasus to conquer but i still have a century to do it
After death of last Courtenay King the Estates General choose Duc de Lorraine as French King
Lorraine and Habsburg unites,
 
So the idea is some empire or Royal line unifies the European continent. We are defining Europe as the the Urals to Ireland. From Sicily to Norway and from Norway to the gulf of Gibraltar and from Gibraltar to the the Caucasus mountains.

The state is allowed to have as much colonial territory or holdings in the Middle East/North Africa or Anatolia as you want.

Make it happen or explain why it can't.

A Mongol Prince and his Horde convert to Christianity. He is invited to restore the Byzantine Empire. He takes Constantinople, and becomes Emperor himself. As Emperor, he has a powerful, efficient army, and establishes an efficient state to support it. (The Mongols are pretty good at that.) Mongol Byzantium whacks the Moslems, regaining Anatolia, and whacks the Slavs, regaining the Balkans. These territories are incorporated into the efficient state. Meanwhile the Khan-Emperor also holds a great dominion north of the Black Sea.

Venice gets into bad trouble in Italy, and yells for help to its nominal overlord. (Venice was originally a Byzantine vassal; that's why it was never part of the Holy Roman Empire. By this time, that relationship had lapsed, but when the Venetians get really desperate, they call it back up.) The Khan-Emperor shows up and rescues them, and then takes over Italy, demoting the Pope to Patriarch of Rome.

Meanwhile... The battle of Las Navas de Tolosa was a resounding victory for the fanatical Almohad Moslems. All four of the Christian kings present were killed, and the Almohads conquered everything south of the Pyrenees. The Almohads began forced conversion of Iberian Christians to Islam. This resulted in a Crusade by France and England, which hit the Almohads hard, but ended with nearly all the Crusaders killed. A generation later, the Almohads surged into France. This time the Holy Roman Emperor joined the Kings of France and England in the Crusade, but the Moslems defeated and killed all three at Bourges, and pressed on to besiege Paris.

The siege was broken by the arrival of the Khan-Emperor and his army, who routed the Moslems. Another Imperial army was in Spain, cleaning up there. The Khan-Emperor decreed that all the redeemed lands must pledge allegiance to the Empire. He also demanded recognition as the new Holy Roman Emperor (or more precisely, that his position as Emperor included that title).

Over the next three centuries, Hungary, Poland, Lithuania, Novgorod, Scandinavia and the British Isles are all absorbed.

Bingo.
 
Avoid Rome's decline, have something happen that severely tones down the migrations. Rome stays united and motivated for conquest due to whatever (religion? a new state ethos? your call) and pushes into Germania and then gradually makes its way to the Steppes after a confrontation with the Mongols. Various tribes look for Rome for protection, get Romanized successfully. Uber-Rome absolutely wrecks Persia, making it a minor power. From here it just snowballs out of proportion, conquest of the Americas, etc.
 
A Mongol Prince and his Horde convert to Christianity. He is invited to restore the Byzantine Empire. He takes Constantinople, and becomes Emperor himself. As Emperor, he has a powerful, efficient army, and establishes an efficient state to support it. (The Mongols are pretty good at that.) Mongol Byzantium whacks the Moslems, regaining Anatolia, and whacks the Slavs, regaining the Balkans. These territories are incorporated into the efficient state. Meanwhile the Khan-Emperor also holds a great dominion north of the Black Sea.

Venice gets into bad trouble in Italy, and yells for help to its nominal overlord. (Venice was originally a Byzantine vassal; that's why it was never part of the Holy Roman Empire. By this time, that relationship had lapsed, but when the Venetians get really desperate, they call it back up.) The Khan-Emperor shows up and rescues them, and then takes over Italy, demoting the Pope to Patriarch of Rome.

Meanwhile... The battle of Las Navas de Tolosa was a resounding victory for the fanatical Almohad Moslems. All four of the Christian kings present were killed, and the Almohads conquered everything south of the Pyrenees. The Almohads began forced conversion of Iberian Christians to Islam. This resulted in a Crusade by France and England, which hit the Almohads hard, but ended with nearly all the Crusaders killed. A generation later, the Almohads surged into France. This time the Holy Roman Emperor joined the Kings of France and England in the Crusade, but the Moslems defeated and killed all three at Bourges, and pressed on to besiege Paris.

The siege was broken by the arrival of the Khan-Emperor and his army, who routed the Moslems. Another Imperial army was in Spain, cleaning up there. The Khan-Emperor decreed that all the redeemed lands must pledge allegiance to the Empire. He also demanded recognition as the new Holy Roman Emperor (or more precisely, that his position as Emperor included that title).

Over the next three centuries, Hungary, Poland, Lithuania, Novgorod, Scandinavia and the British Isles are all absorbed.

Bingo.

Christian hordes are a great idea to do this, but you don't even need to get that complicated. Have them surge into Europe without the Khan dying, obliterating their way through Poland, the HRE and Francia to reach the Atlantic. They then convert to Orthodox Christianity based on Russian contacts and settle in Europe, controlling a state along the entire northern European plain. They marry into the Eastern Roman Empire to defeat the Muslims and eventually unite the two realms. At that point, it's just a matter of conquering the periphery over the next four centuries.
 
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