Suppose that the Ottomans manage to conquer Persia in the 16th or 17th century all the way to Hormuz, giving Khorasan to the Uzbeks and attaining supremacy over the Persian Gulf, to supplement their control over the Red Sea. Most, if not all, of the Arabian Coast also ends up falling into Ottoman influence as a result of this.
With some useful outlets to the Indian Ocean, the Ottoman navy shall be able to harass Iberian trade all over the area.
I ask: can the Ottomans ultimately come to the conclusion that colonies would be an useful addition to their empire? If so, then where can they expand?
India? They could conquer the Portuguese outposts along the coast, and perhaps divide the spoils with their ally, the Mughals.
Aceh? The region produced the valuable commodity of pepper, and was majority Muslim, so the Turks would not find much difficulty in even annexing the place.
Malaya?
Northern Borneo?
Parts of the Philippines?
The Moluccas?
Even some part of Australia?