This paper describes an exploratory study aiming to investigate the existence of distinct groups of social enterprises according to organisational identity dimensions. A taxonomy was developed with a two-step cluster analysis based on the importance attached to both social and market identity by 111 social enterprises acting in Portugal. ANOVA and Chi-square analyses were employed to investigate differences between groups. The taxonomy provides a parsimonious description of four groups of social enterprises and suggests the existence of a trade-off between the involvement and participation of clients/beneficiaries and the geographical scope. The combination of high levels of social identity and market identity is associated with more satisfactory levels of social and financial performance. However, giving prevalence to the social or the market identity seems to lead to lower levels of financial and social performance, respectively.