Please elaborate. My immediate reaction is Occam's Razor makes the idea of multiple distinct selves pretty unlikely. But then I think maybe you're defining self differently than I would, and it's certain that the brain and mind have a certain amount of modularity. Even if our self can be divided into several functioning parts, and even if we are using/ experiencing some part stronger than others, that doesn't seem to be evidence of multiple individual selves. Even when you have modularity that results in some weird behavior, that doesn't suggest multiple selves would be split between the past and present. From science, I think about the fact that say, we can see things in the present and imagine things in the past and I've never heard about them being done by distinct parts of the brain. But the strongest intuitive reason and evidence I'd put forth, would just be my experiences with friends who have PTSD. When undergoing a flashback they don't experience things as if it were a memory of the past. That combined with the lack of evidence that people with/ who get PTSD don't seem to be any different than nuero typicals. (There's some evidence that some people are more likely to get PTSD, but no evidence that anyone is immune.)
In the naive model of the self, where "you" make a decision, and then your body executes that decision, and it's the same "you" every time. And it's true that this is a very simple model, and if we didn't have any other evidence, that's what we would probably go with.
But that model that doesn't explain the Peak-end rule very well -- how is it that a certain experience is worse while experienced, but better when remembered? Similarly, it's hard to explain hyperbolic discounting in terms of a continuous self. And how would self-talk be...
http://www.smbc-comics.com/index.php?db=comics&id=2705
Addresses questions like "If I don't remember, but it definitely happened... who suffered?" in a rather non-obvious way (non-obvious to me, anyway).