In recent years, discussion of the limitations of the standard cross-lagged panel model (CLPM) has increased, and the random intercept cross-lagged panel model (RI-CLPM) has been proposed as an improved approach to modeling. By now, there are some first applications of the model to investigate reciprocal relations in self-concept development. However, a methodological-substantive integration of the model in the context of the three major comparison processes in self-concept development is still missing, and it has not been used to evaluate dimensional and temporal comparison effects. We provide such an integration in self-concept theory and applied the RI-CLPM to investigate social, dimensional, and temporal comparison effects simultaneously. Investigating a sample of 701 German students from the middle of Grade 9 to the middle of Grade 10, we confirmed previous results by finding trait-like stability in science, technology, engineering, and mathematics (STEM) self-concept as well as in STEM and language achievement. We also found evidence for all three comparison effects, but evidence for dimensional comparison effects was only found at the between-person level of the RI-CLPM.