Data envelopment analysis (DEA) is a method for identifying the best practices among peer decision-making units (DMUs). Early DEA models were suited for a production possibility set of positive inputs and outputs. In real setups, some inputs and outputs may be negative. Several past studies have provided methods of dealing with negative data in DEA. Furthermore, the premise of early DEA models was that DMUs are homogeneous, though DMUs may exhibit a network structure with negative input and output values in practice. In this study, we presented semi-oriented radial measure (SORM) network DEA models to assess the system as a whole as well as the first and second Stages. The proposed method was compared with a network bi-directional SORM (DSORM) model. The targets obtained from the SORM network model revealed an improvement from the observed values, whereas some of the Stage 2 targets from the DSORM model revealed reductions from the observed values. An integrated SORM model was used to analyse the overall system at once; a higher discrimination of the DMUs was observed in the model. The models were applied to data from 13 insurance companies in Mauritius. The premium collection Stage (Stage 1) was observed to be the dominant Stage of the insurance companies.