France is more successful in supporting anti-British opposition in India while Portugal expands beyond its traditional outposts in Goa, giving a three-way division of the subcontinent.
As the title implies, your challenge is to have India be divided by the European empires instead of being a singular colony, basically a similar situation to Africa and South East Asia. It can be divided by Britain, France, Portugal, Spain, Netherlands, Belgium, Germany, and/or Italy.
The biggest challenge to any Ottoman colonial attempt would be challenge by superior European forces and if the Ottoman Empire does dedicate resources to colonial atrempt it would weaken them elsewhereWhy not add the Danes/Scandinavia or the Ottomans here? Honestly, I think an Ottomans that develops a colonial-naval interests in the 1600-1700's would be in a good position to pick up some of the decline in Muhgal interests by clientizing the Islamic dynasties of the eastern Indian coast, though this would require a checking of Russia's rise in order to remove the pressure on the Black Sea front so they could afford to turn attention to the Indian Ocean. Establishing a Red Sea-Med connection (Either via some kind of canal or a duel-port system connected by a highly organized and dense system of overland transport) would be helpful, but it could also come about as coming to a stable frontier with Persia or a development along the Red Sea coastal ports.
The Dutch actualy had a relatively decent part of southern India, but managed to lose (and sell/trade) it all. I think part of the reason is that Indonesia was more important for the Dutch. I could see the Dutch keeping and expending in southern India. Especialy if they use Ceylon as a base. So give the Dutch the southern part of India, give the British Bengal and the Ghanges river, give France the eastern part of India and Portugal the western part. That could work, maybe.The dutch could also have more (probably small) parts of south India instead of only Sri Lanka.