Moscow, Calcutta and Istanbul can be city-states. The rest of Russia might be the Khazar Empire or the Ukrainian Empire for example. The rest of India might be just as Balkanized as it was in the 18th century.
So one of the smarter Sultans makes some reforms. He sets down firm rules for succession so there aren't any more civil wars, and the populace is less likely to rebel.
The Ottomans set up colonial outposts in various locales around the Indian Ocean, including Calcutta.
In the same timeline Ukraine took over much of OTL Western and Central Asia, but not Moscow, perhaps. But one of the lesser Ottoman princes falls madly in love with a Moscovite and insists on marrying her and she converts. The city-state of Moscow is small and weak, they don't want to fight a war with the Ottomans and don't want to risk war with Ukraine. The city of Moscow gets deeded to the Ottomans.
Q. Why would the Ottomans *want* Moscow??
A. Um, well, at first, they don't especially want it, but this prince insists on marrying this totally hot'n'sexy princess and you know how troublesome princes are when they don't get their way. Then the Ottomans figure the Moscovites can help the Ottomans expand their territory and influence in the area, get some decent ports along the Baltic maybe and try and keep the Ukrainians from expanding too much into lands where the Ottomans want to expand to...? Does that make any sense at all?

Or the Ukrainian empire takes Constantinople, India remains Balkanized and Ukraine sets up trading posts in the Indian Ocean region...
Or industrialization starts under the Chinese Song Dynasty, the people of India get lots better guns and other stuff than what the Ottomans have.
The Ottoman empire falls, India gets unified and develops zeppellins, balloons, hang gliders, etc. So they don't have to conquer all the territory between India and the Bosporus, or between the Bosporus and Moscow, they just want isolated but useful regions which they can control via the zeppelins.
(In this timeline how soon can they get radios? That would be helpful as well. They just have to get them before the Europeans or Ottomans do.)