This article is a collective position paper from the Wimmics research team, expressing our vision of how Web graph data technologies should evolve in the future in order to ensure a high-level of interoperability between the many types of applications that produce and consume graph data. Wimmics stands for Web-Instrumented Man-Machine Interactions, Communities, and Semantics. We are a joint research team between INRIA Sophia Antipolis-M{é}diterran{é}e and I3S (CNRS and Universit{é} C{ô}te d'Azur). Our challenge is to bridge formal semantics and social semantics on the web. Our research areas are graph-oriented knowledge representation, reasoning and operationalization to model and support actors, actions and interactions in web-based epistemic communities. The application of our research is supporting and fostering interactions in online communities and management of their resources. In this position paper, we emphasize the need to extend the semantic Web standard stack to address and fulfill new graph data needs, as well as the importance of remaining compatible with existing recommendations, in particular the RDF stack, to avoid the painful duplication of models, languages, frameworks, etc. The following sections group motivations for different directions of work and collect reasons for the creation of a working group on RDF 2.0 and other recommendations of the RDF family.