Darwin's 19th century evolutionary theory of descent with modification through natural selection opened up a multidimensional and integrative conceptual space for biology. We explore three dimensions of this space: explanatory pattern, levels of selection, and degree of difference among units of the same type. Each dimension is defined by a respective pair of poles: law and narrative explanation, organismic and hierarchical selection, and variational and essentialist thinking. As a consequence of conceptual debates in the 20th century biological sciences, the poles of each pair came to be seen as mutually exclusive opposites. A significant amount of 21st century research focuses on systems (e.g., genomic, cellular, organismic, and ecological/global). Systemic Darwinism is emerging in this context. It follows a "compositional paradigm" according to which complex systems and their hierarchical networks of parts are the focus of biological investigation. Through the investigation of systems, Systemic Darwinism promises to reintegrate each dimension of Darwin's original logical space. Moreover, this ideally and potentially unified theory of biological ontology coordinates and integrates a plurality of mathematical biological theories (e.g., self-organization/structure, cladistics/history, and evolutionary genetics/function). Integrative Systemic Darwinism requires communal articulation from a plurality of perspectives. Although it is more general than these, it draws on previous advances in Systems Theory, Systems Biology, and Hierarchy Theory. Systemic Darwinism would greatly further bioengineering research and would provide a significantly deeper and more critical understanding of biological reality.