For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
The Book of Laughter and Forgetting is divided into seven parts, each of which—with the exceptions of parts IV and VI—tells a unique story, with its own cast of characters. Since the narrative is not unified, it isn't really possible to divide the work into three acts. Even if we look at the work as a whole, there's no neat or meaningful way to break the movement of the stories into three parts.