This paper presents a multisource and multimethod investigation of the relationship between principals’ strategic cognitive complexity (SCC) and school outcomes assessed by parents, as mediated by teachers’ identification with the school. We have assessed the SCC of 165 school principals, derived from interviews in which they described their strategy and long-term educational vision for the school. A sample of teachers from these Romanian schools (2687 teachers in total, 360 male) reported their identification with the school and a sample of parents (10080 in total, 1658 male) assessed the school academic climate and reported their engagement with the school. We used a non-linear mediation procedure and show that SCC has an inverted U-shaped association with teachers identification with the school that in turn has a positive association with parents’ engagement with the school and their rating of the academic climate. Our results challenge the universality of SCC benefits in schools and point out the importance of exploring diminishing benefits associated with SCC by using multisource data and the “too much of a good thing” theoretical framework as a guide for future research directions in strategic management in schools.