Over the past decades, the definition of system has eluded researchers and practitioners. We reviewed over 100 definitions of system to understand the variations and establish a framework for a widely acceptable system definition or a family of system definitions. There is much common ground in different families of definitions of system, but there are also important and significant ontological differences. Some differences stem from the variety of belief systems and worldviews, while others have risen within particular communities. Both limit the effectiveness of system communities’ efforts to communicate, collaborate, and learn from others’ experience. We consider three ontological elements: (1) a worldview-based framework for typology of different system types and categories, (2) key system concepts that are fundamental to the various system types and categories, and (3) appropriate language for the target audience. In this work, we establish the ontological framework, list key concepts associated with different types of system, and point to a direction for agreeing on an integrated set of system definitions in a neutral language consistent with the framework. The definitions are compatible with both the realist and constructivist worldviews, covering real (physical, concrete) and conceptual (abstract, logical, informatical) systems, which are both human-made (artificial) and naturally occurring, using language acceptable to a wide target stakeholder audience. The contribution of this paper is setting up an ontologically founded framework of system typologies, providing definitions for system, and identifying the issues involved in achieving a widely accepted definition or family of definitions of system.