The evolvability of animal body plans is limited. For instance, strong constraints exist against evolutionary change of early organogenesis, also called the phylotypic stage. Most of the body plan is usually laid out during this stage, and as a consequence, its conservation is implicated in the conservation of body plans. Two hypotheses have been proposed to explain the strong conservation of the phylotypic stage. One states that the conservation reflects a strong interactivity between developmental modules, so that mutations would have many pleiotropic effects, resulting in stabilizing selection against the mutations. The other states that, at least in insects, the conservation is caused by the robustness of a centrally important organizer gene network against mutational changes. I describe how the empirical and theoretical support for the robustness hypothesis is weak, but it is strong for the pleiotropy hypothesis. This highlights the importance of developmental modularity for evolvability. Finally, I discuss how an ancient metazoan constraint on the division of differentiated cells causes the early loss of pluripotentiality of cells. Consequently, the layout of the body plan occurs early, when the embryo is small, and the number of inductive interactions is too limited to allow for effective developmental modularity. Hence, this constraint on simultaneous cell division and differentiation causes another constraint: The one against changes of the phylotypic stage and of the body plan traits that are determined at these stages.