Through a survey addressed to family firms in Northern Italy, we investigate the antecedents and the different outcomes of entrepreneurial behaviour (EB) in family firms. We test a model that determines how factors such as non-economic goals/socioemotional wealth (SEW) dimensions of family managers influence EB and how EB, in turn, affects open innovation choices (i.e., breadth) and innovation performance. We assess the interplay among these variables by means of a structural equation modelling (SEM) model. As concerns the antecedents of EB, findings show a positive influence of the SEW dimensions 'identification with the firm' and 'binding social ties', whereas a negative influence emerges regarding 'emotional attachment among family members'. Moreover, EB enhances openness breadth, and this, in turn, acting as a mediator of the relationship between EB and innovation performance, fosters explorative results.