Organogenesis is a tightly regulated process that has been studied experimentally for decades. We are developing mechanistic models for the morphogenesis of limbs, lungs, and kidneys with a view to integrate available knowledge and to better understand the underlying regulatory logic. In our previous paper on simulating organogenesis in COMSOL (German et al COMSOL Conf Procedings 2011) we discussed methods to efficiently solve such models, predominantly on a static domain. Organ size, however, changes dramatically during development, and tissues are composed of several layers that may expand both together or independently. Moreover, the developing organ are typically embedded in an environment, and diffusional exchange with this environment can affect the patterning process. Here we discuss methods to build and efficiently solve models involving large deformation of composite domains in COMSOL Multiphysics.