Model-driven engineering (MDE) and, in particular, the notion of domain-specific modelling languages (DSMLs) is an increasingly popular approach to systems development. DSMLs are particularly interesting because they allow encoding domain-knowledge into a modelling language and enable full code generation and analysis based on high-level models. However, as a result of the domain-specificity of DSMLs, there is a need for many such languages. This means that their use only becomes economically viable if the development of new DSMLs can be made efficient. One way to achieve this is by reusing functionality across DSMLs. On this background, we are working on techniques for modularising DSMLs into reusable units. Specifically, we focus on DSMLs whose semantics are defined through in-place model transformations. In this paper, we present a formal framework of morphisms between graph-transformation systems (GTSs) that allow us to define a novel technique for conservative extensions of such DSMLs. In particular, we define different behaviour-aware GTS morphisms and prove that they can be used to define conservative extensions of a GTS.