Meta-modelling is central to Model-Driven Engineering. Many meta-modelling notations, approaches and tools have been proposed along the years, which widely vary regarding their supported modelling features. However, current approaches tend to be closed and rigid with respect to the supported concepts and semantics. Moreover, extending the environment with features beyond those natively supported requires highly technical knowledge. This situation hampers flexibility and interoperability of meta-modelling environments. In order to alleviate this situation, we propose open meta-modelling frameworks, which can be extended and configured via meta-object protocols (MOPs). Such environments offer extension points on events like element instantiation, model loading or property access, and enable selecting particular model elements over which the extensions are to be executed. We show how MOP-based mechanisms permit extending meta-modelling frameworks in a flexible way, and allow describing a wide range of meta-modelling concepts. As a proof of concept, we show and compare an implementation in the MetaDepth tool and an aspectbased implementation atop the Eclipse Modelling Framework (EMF). We have evaluated our approach by extending EMF and MetaDepth with modelling services not foreseen initially when they were created. The evaluation shows that MOP-based mechanisms permit extending meta-modelling frameworks in a flexible way, and are powerful enough to support the specification of a broad variety of meta-modelling features.