I have no idea what "multiculturalism" is supposed to mean. For some reason, Galicia didn't work until the Poles and Ukrainians were clearly separated and the Jews gone. No idea why. On the other hand Constantinople worked. But then the Ottomans had a strong hand in their own capital, like Singapore. I think minorities work if there is some similarity so that it won't prevent you from leveraging the full power of your core group of people, whatever that is.
India by the way is a good example. It works... in its own way but I can only see it going up at the moment, it's in a good place. Nigeria is the example
I can give. It doesn't work, it won't work, it never worked. Only human suffering ahead. Ukraine though is the best example. It's like putting us (Romanians) and Magyars together
today. Not a happy ending. Perhaps 200 years ago in the time of Rakoczy (for us and Magyars), or of Catherine the Great (for Ukrainians and Russians) but not today. Similarly, there is a specific timeframe for the Turks to do what needs to be done to keep Greeks on their side (by creating dissension between Greeks and the West, Greek-speaking Greeks and non-Greek-speaking Greeks, by compromise and concessions etc., by instigating some Greeks to fight the rebellious Greeks while providing relief to the civilian Greek population and other possible methods).
Besides these general points, the issues raised by the middle east are not exactly "multiculturalism" (what does that mean, really?).
So send settlers. Displace them. Incentive them to move away from their homelands. Change their culture.
This is what Israel is currently doing in part of the Middle East. The Ottomans were harsh man, but not like this.
The basic problem is different though: It's too much trouble for too little. I've already said, you should keep, perhaps the kurdish bits to protect from Iran. In the rest of the region, if there is a place that is important for the Empire, give power to the tribes, since they're already there and already work (and the Ottomans did just this) and protect them from the other tribes. Basically what W imperialists did, plus with your expert knowledge in the region, drawing borders that would be good for the people of the region themselves. Nothing is gained by incorporating tham in the Empire.
How is this any different from Europe for most of its history?
It's different. Every single place in this world is different from any other. Any single culture is different from any other. People are different, because wwe adapt to our respective environments and the environments are different.
In the Balkans, you'll have a short time of trouble, but after that the Bulgarians in your Empire will not randomly start attaking Greeks. In the A-H Empire, as much as we came to resent the Magyars, an inter-ethnic fight was big news, there were a few proeminent revolts (like Horea's). The Middle East is simply more volatile, for two reasons (1) it's flat; (2) resource pressure is much much higher, there just aren't enough resources for the entire population - the tribes don't go to war just for the fun of it.
Anyway, if you really put your mind to it, I guess there is a way, but I wouldn't do it. Personally, if I were the Emperor, I'd get another odalisque and invest the rest of the money in the Balkans - you can really industrialise the Balkans. Keep influence in the Middle East, of course, but don't get directly involved. My critique is, basically, you're kind of presenting a variant of the W Bush argument - surely the Iraqis can be taught "democracy". The Iraqis had other priorities, more pressing. When you're life is in danger one has to prioritise. Of course Ottoman rule will be better, less intrusive (unless we follow your advice and colonise the region with Slavs, Israeli-style - do you really think that will get the spirits less inflamed?). You can influence the region without geting your hand dirty. Why not save money? You don't really need any more than the Sinai (plus Suez) and a vassal in the Hejaz.
Anyway this is just what I would do. If you're Padisah, you can do as you please, but if you have a Parliament and a Grand Vizier they might make the same geopolitical arguments as I did. In fact, Ataturk made a version of this argument: let's just keep Turkey proper. The great loss was the Balkans and the fact that he was too secular too quick, or just way too secular. Present day Turkey plus the Balkans, with or without a "Greek" compliant minority, and not completely cut out by secularism from the Islamic world (by adopting, for instance the Young Ottoman line), would be very rich. And would have influence on the Islamic world, being able to counter the poisonous Wahhabism. (I think Erdogan was trying to build just that, he's just not up for the job, plus the Balkans are kind of lost for good...)
A QUICK NOTE: By my democracy comment, I don't mean Iraqis are inferior - far from it. I only mean that western systems of government were invented to solve specific European problems. Those problems do not exist in the Middle East. Instead the Middle East has other, different, problems, of its own. I really wish someday someone would make an anonymous poll among the citizens (not all residents just citizens) of Abu Dhabi (who, by the way, are
all just one tribe - just like in all the other emirates, one emirate, one tribe). And ask them who they want for leader. I'm sure they would indicate their current leadership - you see, they consider their Sheykhs legitimate, all the more since they're related to the Emirs (4th, 5th cousin etc. the entire tribe - since they only marry within the tribe they're all related, so corruption is lower, because the Emirs actually care for their citizens). So my idea for the Middle East is a slightly Daoist one. Why oppose nature and try to change things? Just go with the flow and empower the tribes. The Ottomans did this. I only think it was not worth it financially. This thread is about how to make the Ottoman Empire great right, not how to fix the Middle East?...