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Is there any way to know where / when the boats on Amazon river will stop? Or does it depend on passengers and where they want to embark / disembark?

I found information on some blogs that it stops "in at least one port a day", but except bigger ports (Manaus, Santarém and Belem) I haven't found anything.

And is it possible to leave the boat in one of those places and embark another one on the next day (assuming there is something interesting there, I wouldn't stop in a random river Indian community). If I understood correctly, every boat is managed by a different company, so I guess it would be necessary to buy two tickets.

Your ticket is for one boat. In principle, you can not get off, wait, and get on another boat, without purchasing another ticket. Also, the long distance boats only go once or twice per week.

There are several stops along the route that are, for all intents and purposes, guaranteed, but I don't really know how you could determine which ones they are short of calling the companies themselves. These are the stops where many locals will hang out on the dock to try and sell food to the passengers.

In addition to the guaranteed stops, the boats indeed can stop in places convenient for passengers getting off. And, I suppose, getting on.