Spirit Island is my favorite cooperative game, especially with 2 players. It gets around the alpha gamer problem by giving you so many choices and being so asymmetrical that it is hard enough to play your own spirit. This also means that it can bog down with players prone to analysis paralysis and gets harder to find a reasonable plan with more players. I’ve played it with 3 players and that worked pretty well. But I don’t intend to try with 4.
Note that the complexity comes more from the number of options you have and the number of interactions between different game elements, than from the rules.