Over the last decade, the European Grid Infrastructure (EGI) has built a distributed computing and data infrastructure to support over 21,000 researchers from many disciplines with unprecedented data analysis capabilities. EGI builds on the European and national investments and relies on the expertise of EGI.eu - a not-for-profit foundation that provides coordination to the EGI Community, including user groups, EGI.eu participants in the EGI Council, and the other collaborating partners. The mission of EGI-Engage is to accelerate the implementation of the Open Science Commons vision, where researchers from all disciplines have easy and open access to the innovative digital services, data, knowledge and expertise they need for their work. The Open Science Commons is grounded on three pillars: the e-Infrastructure Commons, an ecosystem of key services; the Open Data Commons, where any researcher can access, use and reuse data; and the Knowledge Commons, in which communities have shared ownership of knowledge and participate in the co-development of software and are technically supported to exploit state-of-the-art digital services. EGI-Engage will expand the capabilities offered to scientists (e.g. improved cloud or data services) and the spectrum of its user base by engaging with large Research Infrastructures (RIs), the long-tail of science and industry/SMEs. The main engagement instrument will be a network of eight Competence Centres, where National Grid Initiatives (NGIs), user communities, technology and service providers will join forces to collect requirements, integrate community-specific applications into state-of-the-art services, foster interoperability across e-Infrastructures, and evolve services through a user-centric development model. The project will also coordinate the NGI efforts to support the long-tail of science by developing ad hoc access policies and by providing services and resources that will lower barriers and learning curves.