Models are the central assets in model-driven engineering (MDE), as they are actively used in all phases of software development. Models are built using metamodel-based languages, and so objects in models are typed by a metamodel class. This typing is static, established at creation time, and cannot be changed later. Therefore, objects in MDE are closed and fixed with respect to the class they conform to, the fields they have, and the well-formedness constraints they must comply with. This hampers many MDE activities, like the reuse of model-related artefacts such as transformations, the opportunistic or dynamic combination of metamodels, or the dynamic reconfiguration of models. To alleviate this rigidity, we propose making model objects open so that they can acquire or drop so-called facets . These contribute with a type, fields and constraints to the objects holding them. Facets are defined by regular metamodels, hence being a lightweight extension of standard metamodelling. Facet metamodels may declare usage interfaces , as well as laws that govern the assignment of facets to objects (or classes). This article describes our proposal, reporting on a theory, analysis techniques, and an implementation. The benefits of the approach are validated on the basis of five case studies dealing with annotation models, transformation reuse, multi-view modelling, multi-level modelling, and language product lines.