We present an extension of the Metamorphosis algorithm to align images with different topologies and/or appearances. We propose to restrict/limit the metamorphic intensity additions using a timevarying spatial weight function. It can be used to model prior knowledge about the topological/appearance changes (e.g., tumour/oedema). We show that our method improves the disentanglement between anatomical (i.e., shape) and topological (i.e., appearance) changes, thus improving the registration interpretability and its clinical usefulness. As clinical application, we validated our method using MR brain tumour images from the BraTS 2021 dataset. We showed that our method can better align healthy brain templates to images with brain tumours than existing state-of-the-art methods. Our PyTorch code is freely available here: https://github.com/antonfrancois/Demeter metamorphosis.