Purpose– The purpose of this paper is to contribute to the prior work on social enterprise (SE) model comparisons by exposing the difficulties in producing universally comparative SE models. Furthermore, this paper seeks to trace different dominant stories of SE based on a combined historical and discursive analysis of Australian institutions shaping SE development.Design/methodology/approach– This paper emulates the methodological approach taken by Kerlin (2013) and uses the same indices and measures adopted in this original model comparison. Although the valuable contribution of macro-level model comparison studies to the growing SE knowledge base is noted, it is proposed that categorisations are naturally exclusionary by their design, omitting emergent SE models and their institutional influences. These omissions pose difficulties for recognising and conceptualising hybrid organisations that often traverse institutional boundaries and frameworks (Dohertyet al., 2014). A discourse analysis of SE policies in Australia was used to illustrate how micro-level appraisals of SE models differentiate from, and complement, the macro-level approach.Findings– A combinatory analysis of Australian SEs, based on historical and discursive institutional theories, provides two stories about these organisations. The first story emerges that Australian SEs are partly shaped by institutions, the historical path-dependencies of which are associated with particular SE characteristics. Alternatively, using a discursive lens, the second story of Australian SEs emerges as a political subject, captured within a broader idea (e.g. social inclusion) that is coordinated between political domains and communicated within the public sphere. Therefore, it is argued that a combinatory approach shows SE models as they are, as well as how they might be – contingent on the implementation of identified policies.Research limitations/implications– The major contribution is to critique and extend Kerlin’s (2013) approach by complementing the macro-level study of SE models with an analysis that considers the local-level innovations that drive unique SE models and applications. To enact this, the authors explore how closely macro-level approaches to SE categorisation are the subject of discursive construction, as well as historical events. Consequently, this paper contributes to existing knowledge by advancing existing approaches to SE model studies, illustrating how different stories of SE can be drawn out from combinatory methods and local knowledge.Practical implications– The practical implication arising from this paper is that SE discourses are both a subject of capture and a site of contestation, meaning that various institutional actors play a role in shaping the “reality” of the field.Social implications– The main social implication of this paper is that Australian SEs make a diverse contribution, but there are dangers that the discursive construction of civil society could narrow and constrain this.Originality/value– The novelty inherent in this approach lies in bringing together two frameworks to explore the same field of action. By replicating Kerlin’s (2013) approach and bringing in a discursive analytical framework, it is shown that macro-level studies of SE sectors are enhanced by combinatory methodologies.