Big scientific projects are more likely to practice open science than small projects. Different projects conduct, advocate, develop tools for, or fund open science, and many organizations run multiple projects.
For example, the Allen Institute for Brain Science conducts numerous open science projects while the Center for Open Science has projects to conduct, advocate, and create tools for open science - wsj.com 
Open science is stimulating the emergence of sub-branches such as open synthetic biology and open therapeutics - wikipedia
Organizations have extremely diverse sizes and structures. The Open Knowledge Foundation (OKF) is a global organization sharing large data catalogs, running face to face conferences, and supporting open source software projects.
In contrast, Blue Obelisk is an informal group of chemists and associated cheminformatics projects. The tableau of organizations is dynamic with some organizations becoming defunct, e.g., Science Commons, and new organizations trying to grow, e.g., the Self-Journal of Science.
Common organizing forces include the knowledge domain, type of service provided, and even geography, e.g., OCSDNet's concentration on the developing world.