As in chapter 9, analyses in this chapter are based on mean and covariance structures (MACS). However, whereas the previous application was based on a first-order CFA model, the work in the present chapter focuses on a higher order CFA model. Building on the work of chapter 9, we test for latent mean differences in both the lower and higher order factors of an assessment measure. In reality, however, the work of this chapter addresses an impossible situation and provides alternative approaches to how a researcher might deal with the situation. Essentially, the major interest of this chapter is to obtain a mean structure for a second-order multiplegroup model. However, such models are generally not identified (Lubke, Dolan, & Kelderman, 2001). To obtain any meaningful results, additional specialized constraints have to be added to ordinary mean structure models. Although there is no truly satisfactory solution, the discussion of the issues and an illustration of several approaches on how such constraints might be considered and implemented may be fruitful.