There has recently been renewed scholarly interest in management innovating, the creation of new organizational practices, structures, processes and techniques. We suggest that external involvement in the process of management innovating can transpire in three different ways: direct input from external change agents; prior external experience of internal change agents; and the use of external knowledge sources by internal change agents. We ask whether the type of innovation created (radical or not; systemic or not) depends on the use of these three forms of involvement and whether the forms are substitutes or complements. We empirically investigate this through an archival study of 23 major historical innovations, using in-depth data from a large number of sources in the academic literature. We use three complementary methods of analysis: unstructured qualitative observations, correlational analysis and crisp-set qualitative comparative analysis. We find that the presence of external change agents is associated with systemic and incremental innovations; that the absence of external experience is associated with systemic and radical innovations; and that the presence of external sources of knowledge has no clear effect. Furthermore the three forms of involvement act to a large degree as substitutes. We contribute new theoretical arguments for the facilitators of management innovation, demonstrate the usefulness of an open innovation lens to the study of management innovation, show that management innovating is a relatively complex form of strategic process and highlight how the creation of management innovations is similar to and different from the genesis of other types of innovation.